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1 | 7218-7221 | 03 and 0 15 respectively One of the insured persons meets with an accident What is the probability that
he is a scooter driver |
1 | 7219-7222 | 15 respectively One of the insured persons meets with an accident What is the probability that
he is a scooter driver 8 |
1 | 7220-7223 | One of the insured persons meets with an accident What is the probability that
he is a scooter driver 8 A factory has two machines A and B |
1 | 7221-7224 | What is the probability that
he is a scooter driver 8 A factory has two machines A and B Past record shows that machine A produced
60% of the items of output and machine B produced 40% of the items |
1 | 7222-7225 | 8 A factory has two machines A and B Past record shows that machine A produced
60% of the items of output and machine B produced 40% of the items Further,
2% of the items produced by machine A and 1% produced by machine B were
defective |
1 | 7223-7226 | A factory has two machines A and B Past record shows that machine A produced
60% of the items of output and machine B produced 40% of the items Further,
2% of the items produced by machine A and 1% produced by machine B were
defective All the items are put into one stockpile and then one item is chosen at
random from this and is found to be defective |
1 | 7224-7227 | Past record shows that machine A produced
60% of the items of output and machine B produced 40% of the items Further,
2% of the items produced by machine A and 1% produced by machine B were
defective All the items are put into one stockpile and then one item is chosen at
random from this and is found to be defective What is the probability that it was
produced by machine B |
1 | 7225-7228 | Further,
2% of the items produced by machine A and 1% produced by machine B were
defective All the items are put into one stockpile and then one item is chosen at
random from this and is found to be defective What is the probability that it was
produced by machine B 9 |
1 | 7226-7229 | All the items are put into one stockpile and then one item is chosen at
random from this and is found to be defective What is the probability that it was
produced by machine B 9 Two groups are competing for the position on the Board of directors of a
corporation |
1 | 7227-7230 | What is the probability that it was
produced by machine B 9 Two groups are competing for the position on the Board of directors of a
corporation The probabilities that the first and the second groups will win are
Β© NCERT
not to be republished
PROBABILITY 557
0 |
1 | 7228-7231 | 9 Two groups are competing for the position on the Board of directors of a
corporation The probabilities that the first and the second groups will win are
Β© NCERT
not to be republished
PROBABILITY 557
0 6 and 0 |
1 | 7229-7232 | Two groups are competing for the position on the Board of directors of a
corporation The probabilities that the first and the second groups will win are
Β© NCERT
not to be republished
PROBABILITY 557
0 6 and 0 4 respectively |
1 | 7230-7233 | The probabilities that the first and the second groups will win are
Β© NCERT
not to be republished
PROBABILITY 557
0 6 and 0 4 respectively Further, if the first group wins, the probability of
introducing a new product is 0 |
1 | 7231-7234 | 6 and 0 4 respectively Further, if the first group wins, the probability of
introducing a new product is 0 7 and the corresponding probability is 0 |
1 | 7232-7235 | 4 respectively Further, if the first group wins, the probability of
introducing a new product is 0 7 and the corresponding probability is 0 3 if the
second group wins |
1 | 7233-7236 | Further, if the first group wins, the probability of
introducing a new product is 0 7 and the corresponding probability is 0 3 if the
second group wins Find the probability that the new product introduced was by
the second group |
1 | 7234-7237 | 7 and the corresponding probability is 0 3 if the
second group wins Find the probability that the new product introduced was by
the second group 10 |
1 | 7235-7238 | 3 if the
second group wins Find the probability that the new product introduced was by
the second group 10 Suppose a girl throws a die |
1 | 7236-7239 | Find the probability that the new product introduced was by
the second group 10 Suppose a girl throws a die If she gets a 5 or 6, she tosses a coin three times and
notes the number of heads |
1 | 7237-7240 | 10 Suppose a girl throws a die If she gets a 5 or 6, she tosses a coin three times and
notes the number of heads If she gets 1, 2, 3 or 4, she tosses a coin once and
notes whether a head or tail is obtained |
1 | 7238-7241 | Suppose a girl throws a die If she gets a 5 or 6, she tosses a coin three times and
notes the number of heads If she gets 1, 2, 3 or 4, she tosses a coin once and
notes whether a head or tail is obtained If she obtained exactly one head, what
is the probability that she threw 1, 2, 3 or 4 with the die |
1 | 7239-7242 | If she gets a 5 or 6, she tosses a coin three times and
notes the number of heads If she gets 1, 2, 3 or 4, she tosses a coin once and
notes whether a head or tail is obtained If she obtained exactly one head, what
is the probability that she threw 1, 2, 3 or 4 with the die 11 |
1 | 7240-7243 | If she gets 1, 2, 3 or 4, she tosses a coin once and
notes whether a head or tail is obtained If she obtained exactly one head, what
is the probability that she threw 1, 2, 3 or 4 with the die 11 A manufacturer has three machine operators A, B and C |
1 | 7241-7244 | If she obtained exactly one head, what
is the probability that she threw 1, 2, 3 or 4 with the die 11 A manufacturer has three machine operators A, B and C The first operator A
produces 1% defective items, where as the other two operators B and C pro-
duce 5% and 7% defective items respectively |
1 | 7242-7245 | 11 A manufacturer has three machine operators A, B and C The first operator A
produces 1% defective items, where as the other two operators B and C pro-
duce 5% and 7% defective items respectively A is on the job for 50% of the
time, B is on the job for 30% of the time and C is on the job for 20% of the time |
1 | 7243-7246 | A manufacturer has three machine operators A, B and C The first operator A
produces 1% defective items, where as the other two operators B and C pro-
duce 5% and 7% defective items respectively A is on the job for 50% of the
time, B is on the job for 30% of the time and C is on the job for 20% of the time A defective item is produced, what is the probability that it was produced by A |
1 | 7244-7247 | The first operator A
produces 1% defective items, where as the other two operators B and C pro-
duce 5% and 7% defective items respectively A is on the job for 50% of the
time, B is on the job for 30% of the time and C is on the job for 20% of the time A defective item is produced, what is the probability that it was produced by A 12 |
1 | 7245-7248 | A is on the job for 50% of the
time, B is on the job for 30% of the time and C is on the job for 20% of the time A defective item is produced, what is the probability that it was produced by A 12 A card from a pack of 52 cards is lost |
1 | 7246-7249 | A defective item is produced, what is the probability that it was produced by A 12 A card from a pack of 52 cards is lost From the remaining cards of the pack,
two cards are drawn and are found to be both diamonds |
1 | 7247-7250 | 12 A card from a pack of 52 cards is lost From the remaining cards of the pack,
two cards are drawn and are found to be both diamonds Find the probability of
the lost card being a diamond |
1 | 7248-7251 | A card from a pack of 52 cards is lost From the remaining cards of the pack,
two cards are drawn and are found to be both diamonds Find the probability of
the lost card being a diamond 13 |
1 | 7249-7252 | From the remaining cards of the pack,
two cards are drawn and are found to be both diamonds Find the probability of
the lost card being a diamond 13 Probability that A speaks truth is 4
5 |
1 | 7250-7253 | Find the probability of
the lost card being a diamond 13 Probability that A speaks truth is 4
5 A coin is tossed |
1 | 7251-7254 | 13 Probability that A speaks truth is 4
5 A coin is tossed A reports that a head
appears |
1 | 7252-7255 | Probability that A speaks truth is 4
5 A coin is tossed A reports that a head
appears The probability that actually there was head is
(A) 4
5
(B) 1
2
(C)
51
(D) 2
5
14 |
1 | 7253-7256 | A coin is tossed A reports that a head
appears The probability that actually there was head is
(A) 4
5
(B) 1
2
(C)
51
(D) 2
5
14 If A and B are two events such that A β B and P(B) β 0, then which of the
following is correct |
1 | 7254-7257 | A reports that a head
appears The probability that actually there was head is
(A) 4
5
(B) 1
2
(C)
51
(D) 2
5
14 If A and B are two events such that A β B and P(B) β 0, then which of the
following is correct (A)
P(B)
P(A | B)
P(A)
(B) P(A|B) < P(A)
(C) P(A|B) β₯ P(A)
(D) None of these
13 |
1 | 7255-7258 | The probability that actually there was head is
(A) 4
5
(B) 1
2
(C)
51
(D) 2
5
14 If A and B are two events such that A β B and P(B) β 0, then which of the
following is correct (A)
P(B)
P(A | B)
P(A)
(B) P(A|B) < P(A)
(C) P(A|B) β₯ P(A)
(D) None of these
13 6 Random Variables and its Probability Distributions
We have already learnt about random experiments and formation of sample spaces |
1 | 7256-7259 | If A and B are two events such that A β B and P(B) β 0, then which of the
following is correct (A)
P(B)
P(A | B)
P(A)
(B) P(A|B) < P(A)
(C) P(A|B) β₯ P(A)
(D) None of these
13 6 Random Variables and its Probability Distributions
We have already learnt about random experiments and formation of sample spaces In
most of these experiments, we were not only interested in the particular outcome that
occurs but rather in some number associated with that outcomes as shown in following
examples/experiments |
1 | 7257-7260 | (A)
P(B)
P(A | B)
P(A)
(B) P(A|B) < P(A)
(C) P(A|B) β₯ P(A)
(D) None of these
13 6 Random Variables and its Probability Distributions
We have already learnt about random experiments and formation of sample spaces In
most of these experiments, we were not only interested in the particular outcome that
occurs but rather in some number associated with that outcomes as shown in following
examples/experiments (i)
In tossing two dice, we may be interested in the sum of the numbers on the
two dice |
1 | 7258-7261 | 6 Random Variables and its Probability Distributions
We have already learnt about random experiments and formation of sample spaces In
most of these experiments, we were not only interested in the particular outcome that
occurs but rather in some number associated with that outcomes as shown in following
examples/experiments (i)
In tossing two dice, we may be interested in the sum of the numbers on the
two dice (ii)
In tossing a coin 50 times, we may want the number of heads obtained |
1 | 7259-7262 | In
most of these experiments, we were not only interested in the particular outcome that
occurs but rather in some number associated with that outcomes as shown in following
examples/experiments (i)
In tossing two dice, we may be interested in the sum of the numbers on the
two dice (ii)
In tossing a coin 50 times, we may want the number of heads obtained Β© NCERT
not to be republished
558
MATHEMATICS
(iii)
In the experiment of taking out four articles (one after the other) at random
from a lot of 20 articles in which 6 are defective, we want to know the
number of defectives in the sample of four and not in the particular sequence
of defective and nondefective articles |
1 | 7260-7263 | (i)
In tossing two dice, we may be interested in the sum of the numbers on the
two dice (ii)
In tossing a coin 50 times, we may want the number of heads obtained Β© NCERT
not to be republished
558
MATHEMATICS
(iii)
In the experiment of taking out four articles (one after the other) at random
from a lot of 20 articles in which 6 are defective, we want to know the
number of defectives in the sample of four and not in the particular sequence
of defective and nondefective articles In all of the above experiments, we have a rule which assigns to each outcome of
the experiment a single real number |
1 | 7261-7264 | (ii)
In tossing a coin 50 times, we may want the number of heads obtained Β© NCERT
not to be republished
558
MATHEMATICS
(iii)
In the experiment of taking out four articles (one after the other) at random
from a lot of 20 articles in which 6 are defective, we want to know the
number of defectives in the sample of four and not in the particular sequence
of defective and nondefective articles In all of the above experiments, we have a rule which assigns to each outcome of
the experiment a single real number This single real number may vary with different
outcomes of the experiment |
1 | 7262-7265 | Β© NCERT
not to be republished
558
MATHEMATICS
(iii)
In the experiment of taking out four articles (one after the other) at random
from a lot of 20 articles in which 6 are defective, we want to know the
number of defectives in the sample of four and not in the particular sequence
of defective and nondefective articles In all of the above experiments, we have a rule which assigns to each outcome of
the experiment a single real number This single real number may vary with different
outcomes of the experiment Hence, it is a variable |
1 | 7263-7266 | In all of the above experiments, we have a rule which assigns to each outcome of
the experiment a single real number This single real number may vary with different
outcomes of the experiment Hence, it is a variable Also its value depends upon the
outcome of a random experiment and, hence, is called random variable |
1 | 7264-7267 | This single real number may vary with different
outcomes of the experiment Hence, it is a variable Also its value depends upon the
outcome of a random experiment and, hence, is called random variable A random
variable is usually denoted by X |
1 | 7265-7268 | Hence, it is a variable Also its value depends upon the
outcome of a random experiment and, hence, is called random variable A random
variable is usually denoted by X If you recall the definition of a function, you will realise that the random variable X
is really speaking a function whose domain is the set of outcomes (or sample space) of
a random experiment |
1 | 7266-7269 | Also its value depends upon the
outcome of a random experiment and, hence, is called random variable A random
variable is usually denoted by X If you recall the definition of a function, you will realise that the random variable X
is really speaking a function whose domain is the set of outcomes (or sample space) of
a random experiment A random variable can take any real value, therefore, its
co-domain is the set of real numbers |
1 | 7267-7270 | A random
variable is usually denoted by X If you recall the definition of a function, you will realise that the random variable X
is really speaking a function whose domain is the set of outcomes (or sample space) of
a random experiment A random variable can take any real value, therefore, its
co-domain is the set of real numbers Hence, a random variable can be defined as
follows :
Definition 4 A random variable is a real valued function whose domain is the sample
space of a random experiment |
1 | 7268-7271 | If you recall the definition of a function, you will realise that the random variable X
is really speaking a function whose domain is the set of outcomes (or sample space) of
a random experiment A random variable can take any real value, therefore, its
co-domain is the set of real numbers Hence, a random variable can be defined as
follows :
Definition 4 A random variable is a real valued function whose domain is the sample
space of a random experiment For example, let us consider the experiment of tossing a coin two times in succession |
1 | 7269-7272 | A random variable can take any real value, therefore, its
co-domain is the set of real numbers Hence, a random variable can be defined as
follows :
Definition 4 A random variable is a real valued function whose domain is the sample
space of a random experiment For example, let us consider the experiment of tossing a coin two times in succession The sample space of the experiment is S = {HH, HT, TH, TT} |
1 | 7270-7273 | Hence, a random variable can be defined as
follows :
Definition 4 A random variable is a real valued function whose domain is the sample
space of a random experiment For example, let us consider the experiment of tossing a coin two times in succession The sample space of the experiment is S = {HH, HT, TH, TT} If X denotes the number of heads obtained, then X is a random variable and for
each outcome, its value is as given below :
X(HH) = 2, X (HT) = 1, X (TH) = 1, X (TT) = 0 |
1 | 7271-7274 | For example, let us consider the experiment of tossing a coin two times in succession The sample space of the experiment is S = {HH, HT, TH, TT} If X denotes the number of heads obtained, then X is a random variable and for
each outcome, its value is as given below :
X(HH) = 2, X (HT) = 1, X (TH) = 1, X (TT) = 0 More than one random variables can be defined on the same sample space |
1 | 7272-7275 | The sample space of the experiment is S = {HH, HT, TH, TT} If X denotes the number of heads obtained, then X is a random variable and for
each outcome, its value is as given below :
X(HH) = 2, X (HT) = 1, X (TH) = 1, X (TT) = 0 More than one random variables can be defined on the same sample space For
example, let Y denote the number of heads minus the number of tails for each outcome
of the above sample space S |
1 | 7273-7276 | If X denotes the number of heads obtained, then X is a random variable and for
each outcome, its value is as given below :
X(HH) = 2, X (HT) = 1, X (TH) = 1, X (TT) = 0 More than one random variables can be defined on the same sample space For
example, let Y denote the number of heads minus the number of tails for each outcome
of the above sample space S Then
Y(HH) = 2, Y (HT) = 0, Y (TH) = 0, Y (TT) = β 2 |
1 | 7274-7277 | More than one random variables can be defined on the same sample space For
example, let Y denote the number of heads minus the number of tails for each outcome
of the above sample space S Then
Y(HH) = 2, Y (HT) = 0, Y (TH) = 0, Y (TT) = β 2 Thus, X and Y are two different random variables defined on the same sample
space S |
1 | 7275-7278 | For
example, let Y denote the number of heads minus the number of tails for each outcome
of the above sample space S Then
Y(HH) = 2, Y (HT) = 0, Y (TH) = 0, Y (TT) = β 2 Thus, X and Y are two different random variables defined on the same sample
space S Example 22 A person plays a game of tossing a coin thrice |
1 | 7276-7279 | Then
Y(HH) = 2, Y (HT) = 0, Y (TH) = 0, Y (TT) = β 2 Thus, X and Y are two different random variables defined on the same sample
space S Example 22 A person plays a game of tossing a coin thrice For each head, he is
given Rs 2 by the organiser of the game and for each tail, he has to give Rs 1 |
1 | 7277-7280 | Thus, X and Y are two different random variables defined on the same sample
space S Example 22 A person plays a game of tossing a coin thrice For each head, he is
given Rs 2 by the organiser of the game and for each tail, he has to give Rs 1 50 to the
organiser |
1 | 7278-7281 | Example 22 A person plays a game of tossing a coin thrice For each head, he is
given Rs 2 by the organiser of the game and for each tail, he has to give Rs 1 50 to the
organiser Let X denote the amount gained or lost by the person |
1 | 7279-7282 | For each head, he is
given Rs 2 by the organiser of the game and for each tail, he has to give Rs 1 50 to the
organiser Let X denote the amount gained or lost by the person Show that X is a
random variable and exhibit it as a function on the sample space of the experiment |
1 | 7280-7283 | 50 to the
organiser Let X denote the amount gained or lost by the person Show that X is a
random variable and exhibit it as a function on the sample space of the experiment Solution X is a number whose values are defined on the outcomes of a random
experiment |
1 | 7281-7284 | Let X denote the amount gained or lost by the person Show that X is a
random variable and exhibit it as a function on the sample space of the experiment Solution X is a number whose values are defined on the outcomes of a random
experiment Therefore, X is a random variable |
1 | 7282-7285 | Show that X is a
random variable and exhibit it as a function on the sample space of the experiment Solution X is a number whose values are defined on the outcomes of a random
experiment Therefore, X is a random variable Now, sample space of the experiment is
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Β© NCERT
not to be republished
PROBABILITY 559
Then
X (HHH) = Rs (2 Γ 3) = Rs 6
X(HHT) = X (HTH) = X(THH) = Rs (2 Γ 2 β 1 Γ 1 |
1 | 7283-7286 | Solution X is a number whose values are defined on the outcomes of a random
experiment Therefore, X is a random variable Now, sample space of the experiment is
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Β© NCERT
not to be republished
PROBABILITY 559
Then
X (HHH) = Rs (2 Γ 3) = Rs 6
X(HHT) = X (HTH) = X(THH) = Rs (2 Γ 2 β 1 Γ 1 50) = Rs 2 |
1 | 7284-7287 | Therefore, X is a random variable Now, sample space of the experiment is
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Β© NCERT
not to be republished
PROBABILITY 559
Then
X (HHH) = Rs (2 Γ 3) = Rs 6
X(HHT) = X (HTH) = X(THH) = Rs (2 Γ 2 β 1 Γ 1 50) = Rs 2 50
X(HTT) = X(THT) = (TTH) = Rs (1 Γ 2) β (2 Γ 1 |
1 | 7285-7288 | Now, sample space of the experiment is
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Β© NCERT
not to be republished
PROBABILITY 559
Then
X (HHH) = Rs (2 Γ 3) = Rs 6
X(HHT) = X (HTH) = X(THH) = Rs (2 Γ 2 β 1 Γ 1 50) = Rs 2 50
X(HTT) = X(THT) = (TTH) = Rs (1 Γ 2) β (2 Γ 1 50) = β Re 1
and
X(TTT) = β Rs (3 Γ 1 |
1 | 7286-7289 | 50) = Rs 2 50
X(HTT) = X(THT) = (TTH) = Rs (1 Γ 2) β (2 Γ 1 50) = β Re 1
and
X(TTT) = β Rs (3 Γ 1 50) = β Rs 4 |
1 | 7287-7290 | 50
X(HTT) = X(THT) = (TTH) = Rs (1 Γ 2) β (2 Γ 1 50) = β Re 1
and
X(TTT) = β Rs (3 Γ 1 50) = β Rs 4 50
where, minus sign shows the loss to the player |
1 | 7288-7291 | 50) = β Re 1
and
X(TTT) = β Rs (3 Γ 1 50) = β Rs 4 50
where, minus sign shows the loss to the player Thus, for each element of the sample
isspace, X takes a unique value, hence, X is a function on the sample space whose range
{β1, 2 |
1 | 7289-7292 | 50) = β Rs 4 50
where, minus sign shows the loss to the player Thus, for each element of the sample
isspace, X takes a unique value, hence, X is a function on the sample space whose range
{β1, 2 50, β 4 |
1 | 7290-7293 | 50
where, minus sign shows the loss to the player Thus, for each element of the sample
isspace, X takes a unique value, hence, X is a function on the sample space whose range
{β1, 2 50, β 4 50, 6}
Example 23 A bag contains 2 white and 1 red balls |
1 | 7291-7294 | Thus, for each element of the sample
isspace, X takes a unique value, hence, X is a function on the sample space whose range
{β1, 2 50, β 4 50, 6}
Example 23 A bag contains 2 white and 1 red balls One ball is drawn at random and
then put back in the box after noting its colour |
1 | 7292-7295 | 50, β 4 50, 6}
Example 23 A bag contains 2 white and 1 red balls One ball is drawn at random and
then put back in the box after noting its colour The process is repeated again |
1 | 7293-7296 | 50, 6}
Example 23 A bag contains 2 white and 1 red balls One ball is drawn at random and
then put back in the box after noting its colour The process is repeated again If X
denotes the number of red balls recorded in the two draws, describe X |
1 | 7294-7297 | One ball is drawn at random and
then put back in the box after noting its colour The process is repeated again If X
denotes the number of red balls recorded in the two draws, describe X Solution Let the balls in the bag be denoted by w1, w2, r |
1 | 7295-7298 | The process is repeated again If X
denotes the number of red balls recorded in the two draws, describe X Solution Let the balls in the bag be denoted by w1, w2, r Then the sample space is
S = {w1 w1, w1 w2, w2 w2, w2 w1, w1 r, w2 r, r w1, r w2, r r}
Now, for
Ο β S
X (Ο) = number of red balls
Therefore
X({w1 w1}) = X({w1 w2}) = X({w2 w2}) = X({w2 w1}) = 0
X({w1 r}) = X({w2 r}) = X({r w1}) = X({r w2}) = 1 and X({r r}) = 2
Thus, X is a random variable which can take values 0, 1 or 2 |
1 | 7296-7299 | If X
denotes the number of red balls recorded in the two draws, describe X Solution Let the balls in the bag be denoted by w1, w2, r Then the sample space is
S = {w1 w1, w1 w2, w2 w2, w2 w1, w1 r, w2 r, r w1, r w2, r r}
Now, for
Ο β S
X (Ο) = number of red balls
Therefore
X({w1 w1}) = X({w1 w2}) = X({w2 w2}) = X({w2 w1}) = 0
X({w1 r}) = X({w2 r}) = X({r w1}) = X({r w2}) = 1 and X({r r}) = 2
Thus, X is a random variable which can take values 0, 1 or 2 13 |
1 | 7297-7300 | Solution Let the balls in the bag be denoted by w1, w2, r Then the sample space is
S = {w1 w1, w1 w2, w2 w2, w2 w1, w1 r, w2 r, r w1, r w2, r r}
Now, for
Ο β S
X (Ο) = number of red balls
Therefore
X({w1 w1}) = X({w1 w2}) = X({w2 w2}) = X({w2 w1}) = 0
X({w1 r}) = X({w2 r}) = X({r w1}) = X({r w2}) = 1 and X({r r}) = 2
Thus, X is a random variable which can take values 0, 1 or 2 13 6 |
1 | 7298-7301 | Then the sample space is
S = {w1 w1, w1 w2, w2 w2, w2 w1, w1 r, w2 r, r w1, r w2, r r}
Now, for
Ο β S
X (Ο) = number of red balls
Therefore
X({w1 w1}) = X({w1 w2}) = X({w2 w2}) = X({w2 w1}) = 0
X({w1 r}) = X({w2 r}) = X({r w1}) = X({r w2}) = 1 and X({r r}) = 2
Thus, X is a random variable which can take values 0, 1 or 2 13 6 1 Probability distribution of a random variable
Let us look at the experiment of selecting one family out of ten families f1, f2 , |
1 | 7299-7302 | 13 6 1 Probability distribution of a random variable
Let us look at the experiment of selecting one family out of ten families f1, f2 , , f10 in
such a manner that each family is equally likely to be selected |
1 | 7300-7303 | 6 1 Probability distribution of a random variable
Let us look at the experiment of selecting one family out of ten families f1, f2 , , f10 in
such a manner that each family is equally likely to be selected Let the families f1, f2, |
1 | 7301-7304 | 1 Probability distribution of a random variable
Let us look at the experiment of selecting one family out of ten families f1, f2 , , f10 in
such a manner that each family is equally likely to be selected Let the families f1, f2, , f10 have 3, 4, 3, 2, 5, 4, 3, 6, 4, 5 members, respectively |
1 | 7302-7305 | , f10 in
such a manner that each family is equally likely to be selected Let the families f1, f2, , f10 have 3, 4, 3, 2, 5, 4, 3, 6, 4, 5 members, respectively Let us select a family and note down the number of members in the family denoting
X |
1 | 7303-7306 | Let the families f1, f2, , f10 have 3, 4, 3, 2, 5, 4, 3, 6, 4, 5 members, respectively Let us select a family and note down the number of members in the family denoting
X Clearly, X is a random variable defined as below :
X(f1) = 3, X(f2) = 4, X(f3) = 3, X(f4) = 2, X(f5) = 5,
X(f6) = 4, X(f7) = 3, X(f8) = 6, X(f9) = 4, X(f10) = 5
Thus, X can take any value 2,3,4,5 or 6 depending upon which family is selected |
1 | 7304-7307 | , f10 have 3, 4, 3, 2, 5, 4, 3, 6, 4, 5 members, respectively Let us select a family and note down the number of members in the family denoting
X Clearly, X is a random variable defined as below :
X(f1) = 3, X(f2) = 4, X(f3) = 3, X(f4) = 2, X(f5) = 5,
X(f6) = 4, X(f7) = 3, X(f8) = 6, X(f9) = 4, X(f10) = 5
Thus, X can take any value 2,3,4,5 or 6 depending upon which family is selected Now, X will take the value 2 when the family f4 is selected |
1 | 7305-7308 | Let us select a family and note down the number of members in the family denoting
X Clearly, X is a random variable defined as below :
X(f1) = 3, X(f2) = 4, X(f3) = 3, X(f4) = 2, X(f5) = 5,
X(f6) = 4, X(f7) = 3, X(f8) = 6, X(f9) = 4, X(f10) = 5
Thus, X can take any value 2,3,4,5 or 6 depending upon which family is selected Now, X will take the value 2 when the family f4 is selected X can take the value
3 when any one of the families f1, f3, f7 is selected |
1 | 7306-7309 | Clearly, X is a random variable defined as below :
X(f1) = 3, X(f2) = 4, X(f3) = 3, X(f4) = 2, X(f5) = 5,
X(f6) = 4, X(f7) = 3, X(f8) = 6, X(f9) = 4, X(f10) = 5
Thus, X can take any value 2,3,4,5 or 6 depending upon which family is selected Now, X will take the value 2 when the family f4 is selected X can take the value
3 when any one of the families f1, f3, f7 is selected Similarly,
X = 4, when family f2, f6 or f9 is selected,
X = 5, when family f5 or f10 is selected
and
X = 6, when family f8 is selected |
1 | 7307-7310 | Now, X will take the value 2 when the family f4 is selected X can take the value
3 when any one of the families f1, f3, f7 is selected Similarly,
X = 4, when family f2, f6 or f9 is selected,
X = 5, when family f5 or f10 is selected
and
X = 6, when family f8 is selected Β© NCERT
not to be republished
560
MATHEMATICS
Since we had assumed that each family is equally likely to be selected, the probability
that family f4 is selected is 1
10 |
1 | 7308-7311 | X can take the value
3 when any one of the families f1, f3, f7 is selected Similarly,
X = 4, when family f2, f6 or f9 is selected,
X = 5, when family f5 or f10 is selected
and
X = 6, when family f8 is selected Β© NCERT
not to be republished
560
MATHEMATICS
Since we had assumed that each family is equally likely to be selected, the probability
that family f4 is selected is 1
10 Thus, the probability that X can take the value 2 is 1
10 |
1 | 7309-7312 | Similarly,
X = 4, when family f2, f6 or f9 is selected,
X = 5, when family f5 or f10 is selected
and
X = 6, when family f8 is selected Β© NCERT
not to be republished
560
MATHEMATICS
Since we had assumed that each family is equally likely to be selected, the probability
that family f4 is selected is 1
10 Thus, the probability that X can take the value 2 is 1
10 We write P(X = 2) = 1
10
Also, the probability that any one of the families f1, f3 or f7 is selected is
P({f1, f3, f7}) = 3
10
Thus, the probability that X can take the value 3 = 3
10
We write
P(X = 3) = 3
10
Similarly, we obtain
P(X = 4) = P({f2, f6, f9}) = 3
10
P(X = 5) = P({f5, f10}) = 2
10
and
P(X = 6) = P({f8}) = 1
10
Such a description giving the values of the random variable along with the
corresponding probabilities is called the probability distribution of the random
variable X |
1 | 7310-7313 | Β© NCERT
not to be republished
560
MATHEMATICS
Since we had assumed that each family is equally likely to be selected, the probability
that family f4 is selected is 1
10 Thus, the probability that X can take the value 2 is 1
10 We write P(X = 2) = 1
10
Also, the probability that any one of the families f1, f3 or f7 is selected is
P({f1, f3, f7}) = 3
10
Thus, the probability that X can take the value 3 = 3
10
We write
P(X = 3) = 3
10
Similarly, we obtain
P(X = 4) = P({f2, f6, f9}) = 3
10
P(X = 5) = P({f5, f10}) = 2
10
and
P(X = 6) = P({f8}) = 1
10
Such a description giving the values of the random variable along with the
corresponding probabilities is called the probability distribution of the random
variable X In general, the probability distribution of a random variable X is defined as follows:
Definition 5 The probability distribution of a random variable X is the system of numbers
X
:
x1
x2 |
1 | 7311-7314 | Thus, the probability that X can take the value 2 is 1
10 We write P(X = 2) = 1
10
Also, the probability that any one of the families f1, f3 or f7 is selected is
P({f1, f3, f7}) = 3
10
Thus, the probability that X can take the value 3 = 3
10
We write
P(X = 3) = 3
10
Similarly, we obtain
P(X = 4) = P({f2, f6, f9}) = 3
10
P(X = 5) = P({f5, f10}) = 2
10
and
P(X = 6) = P({f8}) = 1
10
Such a description giving the values of the random variable along with the
corresponding probabilities is called the probability distribution of the random
variable X In general, the probability distribution of a random variable X is defined as follows:
Definition 5 The probability distribution of a random variable X is the system of numbers
X
:
x1
x2 xn
P(X)
:
p 1
p 2 |
1 | 7312-7315 | We write P(X = 2) = 1
10
Also, the probability that any one of the families f1, f3 or f7 is selected is
P({f1, f3, f7}) = 3
10
Thus, the probability that X can take the value 3 = 3
10
We write
P(X = 3) = 3
10
Similarly, we obtain
P(X = 4) = P({f2, f6, f9}) = 3
10
P(X = 5) = P({f5, f10}) = 2
10
and
P(X = 6) = P({f8}) = 1
10
Such a description giving the values of the random variable along with the
corresponding probabilities is called the probability distribution of the random
variable X In general, the probability distribution of a random variable X is defined as follows:
Definition 5 The probability distribution of a random variable X is the system of numbers
X
:
x1
x2 xn
P(X)
:
p 1
p 2 p n
where,
1
0,
n
i
i
i
p
p
= 1, i = 1, 2, |
1 | 7313-7316 | In general, the probability distribution of a random variable X is defined as follows:
Definition 5 The probability distribution of a random variable X is the system of numbers
X
:
x1
x2 xn
P(X)
:
p 1
p 2 p n
where,
1
0,
n
i
i
i
p
p
= 1, i = 1, 2, , n
The real numbers x1, x2, |
1 | 7314-7317 | xn
P(X)
:
p 1
p 2 p n
where,
1
0,
n
i
i
i
p
p
= 1, i = 1, 2, , n
The real numbers x1, x2, , xn are the possible values of the random variable X and
pi (i = 1,2, |
1 | 7315-7318 | p n
where,
1
0,
n
i
i
i
p
p
= 1, i = 1, 2, , n
The real numbers x1, x2, , xn are the possible values of the random variable X and
pi (i = 1,2, , n) is the probability of the random variable X taking the value xi i |
1 | 7316-7319 | , n
The real numbers x1, x2, , xn are the possible values of the random variable X and
pi (i = 1,2, , n) is the probability of the random variable X taking the value xi i e |
1 | 7317-7320 | , xn are the possible values of the random variable X and
pi (i = 1,2, , n) is the probability of the random variable X taking the value xi i e ,
P(X = xi) = pi
Β© NCERT
not to be republished
PROBABILITY 561
οΏ½Note If xi is one of the possible values of a random variable X, the statement
X = xi is true only at some point (s) of the sample space |
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