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1 | 7418-7421 | State which of the following are not the probability distributions of a random
variable Give reasons for your answer (i)
X
0
1
2
P(X)
0 4
0 |
1 | 7419-7422 | Give reasons for your answer (i)
X
0
1
2
P(X)
0 4
0 4
0 |
1 | 7420-7423 | (i)
X
0
1
2
P(X)
0 4
0 4
0 2
(ii)
X
0
1
2
3
4
P(X)
0 |
1 | 7421-7424 | 4
0 4
0 2
(ii)
X
0
1
2
3
4
P(X)
0 1
0 |
1 | 7422-7425 | 4
0 2
(ii)
X
0
1
2
3
4
P(X)
0 1
0 5
0 |
1 | 7423-7426 | 2
(ii)
X
0
1
2
3
4
P(X)
0 1
0 5
0 2
– 0 |
1 | 7424-7427 | 1
0 5
0 2
– 0 1
0 |
1 | 7425-7428 | 5
0 2
– 0 1
0 3
© NCERT
not to be republished
570
MATHEMATICS
(iii)
Y
– 1
0
1
P(Y)
0 |
1 | 7426-7429 | 2
– 0 1
0 3
© NCERT
not to be republished
570
MATHEMATICS
(iii)
Y
– 1
0
1
P(Y)
0 6
0 |
1 | 7427-7430 | 1
0 3
© NCERT
not to be republished
570
MATHEMATICS
(iii)
Y
– 1
0
1
P(Y)
0 6
0 1
0 |
1 | 7428-7431 | 3
© NCERT
not to be republished
570
MATHEMATICS
(iii)
Y
– 1
0
1
P(Y)
0 6
0 1
0 2
(iv)
Z
3
2
1
0
–1
P(Z)
0 |
1 | 7429-7432 | 6
0 1
0 2
(iv)
Z
3
2
1
0
–1
P(Z)
0 3
0 |
1 | 7430-7433 | 1
0 2
(iv)
Z
3
2
1
0
–1
P(Z)
0 3
0 2
0 |
1 | 7431-7434 | 2
(iv)
Z
3
2
1
0
–1
P(Z)
0 3
0 2
0 4
0 |
1 | 7432-7435 | 3
0 2
0 4
0 1
0 |
1 | 7433-7436 | 2
0 4
0 1
0 05
2 |
1 | 7434-7437 | 4
0 1
0 05
2 An urn contains 5 red and 2 black balls |
1 | 7435-7438 | 1
0 05
2 An urn contains 5 red and 2 black balls Two balls are randomly drawn |
1 | 7436-7439 | 05
2 An urn contains 5 red and 2 black balls Two balls are randomly drawn Let X
represent the number of black balls |
1 | 7437-7440 | An urn contains 5 red and 2 black balls Two balls are randomly drawn Let X
represent the number of black balls What are the possible values of X |
1 | 7438-7441 | Two balls are randomly drawn Let X
represent the number of black balls What are the possible values of X Is X a
random variable |
1 | 7439-7442 | Let X
represent the number of black balls What are the possible values of X Is X a
random variable 3 |
1 | 7440-7443 | What are the possible values of X Is X a
random variable 3 Let X represent the difference between the number of heads and the number of
tails obtained when a coin is tossed 6 times |
1 | 7441-7444 | Is X a
random variable 3 Let X represent the difference between the number of heads and the number of
tails obtained when a coin is tossed 6 times What are possible values of X |
1 | 7442-7445 | 3 Let X represent the difference between the number of heads and the number of
tails obtained when a coin is tossed 6 times What are possible values of X 4 |
1 | 7443-7446 | Let X represent the difference between the number of heads and the number of
tails obtained when a coin is tossed 6 times What are possible values of X 4 Find the probability distribution of
(i) number of heads in two tosses of a coin |
1 | 7444-7447 | What are possible values of X 4 Find the probability distribution of
(i) number of heads in two tosses of a coin (ii) number of tails in the simultaneous tosses of three coins |
1 | 7445-7448 | 4 Find the probability distribution of
(i) number of heads in two tosses of a coin (ii) number of tails in the simultaneous tosses of three coins (iii) number of heads in four tosses of a coin |
1 | 7446-7449 | Find the probability distribution of
(i) number of heads in two tosses of a coin (ii) number of tails in the simultaneous tosses of three coins (iii) number of heads in four tosses of a coin 5 |
1 | 7447-7450 | (ii) number of tails in the simultaneous tosses of three coins (iii) number of heads in four tosses of a coin 5 Find the probability distribution of the number of successes in two tosses of a die,
where a success is defined as
(i) number greater than 4
(ii) six appears on at least one die
6 |
1 | 7448-7451 | (iii) number of heads in four tosses of a coin 5 Find the probability distribution of the number of successes in two tosses of a die,
where a success is defined as
(i) number greater than 4
(ii) six appears on at least one die
6 From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn
at random with replacement |
1 | 7449-7452 | 5 Find the probability distribution of the number of successes in two tosses of a die,
where a success is defined as
(i) number greater than 4
(ii) six appears on at least one die
6 From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn
at random with replacement Find the probability distribution of the number of
defective bulbs |
1 | 7450-7453 | Find the probability distribution of the number of successes in two tosses of a die,
where a success is defined as
(i) number greater than 4
(ii) six appears on at least one die
6 From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn
at random with replacement Find the probability distribution of the number of
defective bulbs 7 |
1 | 7451-7454 | From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn
at random with replacement Find the probability distribution of the number of
defective bulbs 7 A coin is biased so that the head is 3 times as likely to occur as tail |
1 | 7452-7455 | Find the probability distribution of the number of
defective bulbs 7 A coin is biased so that the head is 3 times as likely to occur as tail If the coin is
tossed twice, find the probability distribution of number of tails |
1 | 7453-7456 | 7 A coin is biased so that the head is 3 times as likely to occur as tail If the coin is
tossed twice, find the probability distribution of number of tails 8 |
1 | 7454-7457 | A coin is biased so that the head is 3 times as likely to occur as tail If the coin is
tossed twice, find the probability distribution of number of tails 8 A random variable X has the following probability distribution:
X
0
1
2
3
4
5
6
7
P(X)
0
k
2k
2k
3k
k 2 2k2 7k2+k
Determine
(i) k
(ii) P(X < 3)
(iii) P(X > 6)
(iv) P(0 < X < 3)
© NCERT
not to be republished
PROBABILITY 571
9 |
1 | 7455-7458 | If the coin is
tossed twice, find the probability distribution of number of tails 8 A random variable X has the following probability distribution:
X
0
1
2
3
4
5
6
7
P(X)
0
k
2k
2k
3k
k 2 2k2 7k2+k
Determine
(i) k
(ii) P(X < 3)
(iii) P(X > 6)
(iv) P(0 < X < 3)
© NCERT
not to be republished
PROBABILITY 571
9 The random variable X has a probability distribution P(X) of the following form,
where k is some number :
P(X) =
,
0
2 ,
1
3 ,
2
0, otherwise
k
if x
k if x
k if x
=
⎪⎧
=
⎪⎨
=
⎪
⎪⎩
(a)
Determine the value of k |
1 | 7456-7459 | 8 A random variable X has the following probability distribution:
X
0
1
2
3
4
5
6
7
P(X)
0
k
2k
2k
3k
k 2 2k2 7k2+k
Determine
(i) k
(ii) P(X < 3)
(iii) P(X > 6)
(iv) P(0 < X < 3)
© NCERT
not to be republished
PROBABILITY 571
9 The random variable X has a probability distribution P(X) of the following form,
where k is some number :
P(X) =
,
0
2 ,
1
3 ,
2
0, otherwise
k
if x
k if x
k if x
=
⎪⎧
=
⎪⎨
=
⎪
⎪⎩
(a)
Determine the value of k (b)
Find P (X < 2), P (X ≤ 2), P(X ≥ 2) |
1 | 7457-7460 | A random variable X has the following probability distribution:
X
0
1
2
3
4
5
6
7
P(X)
0
k
2k
2k
3k
k 2 2k2 7k2+k
Determine
(i) k
(ii) P(X < 3)
(iii) P(X > 6)
(iv) P(0 < X < 3)
© NCERT
not to be republished
PROBABILITY 571
9 The random variable X has a probability distribution P(X) of the following form,
where k is some number :
P(X) =
,
0
2 ,
1
3 ,
2
0, otherwise
k
if x
k if x
k if x
=
⎪⎧
=
⎪⎨
=
⎪
⎪⎩
(a)
Determine the value of k (b)
Find P (X < 2), P (X ≤ 2), P(X ≥ 2) 10 |
1 | 7458-7461 | The random variable X has a probability distribution P(X) of the following form,
where k is some number :
P(X) =
,
0
2 ,
1
3 ,
2
0, otherwise
k
if x
k if x
k if x
=
⎪⎧
=
⎪⎨
=
⎪
⎪⎩
(a)
Determine the value of k (b)
Find P (X < 2), P (X ≤ 2), P(X ≥ 2) 10 Find the mean number of heads in three tosses of a fair coin |
1 | 7459-7462 | (b)
Find P (X < 2), P (X ≤ 2), P(X ≥ 2) 10 Find the mean number of heads in three tosses of a fair coin 11 |
1 | 7460-7463 | 10 Find the mean number of heads in three tosses of a fair coin 11 Two dice are thrown simultaneously |
1 | 7461-7464 | Find the mean number of heads in three tosses of a fair coin 11 Two dice are thrown simultaneously If X denotes the number of sixes, find the
expectation of X |
1 | 7462-7465 | 11 Two dice are thrown simultaneously If X denotes the number of sixes, find the
expectation of X 12 |
1 | 7463-7466 | Two dice are thrown simultaneously If X denotes the number of sixes, find the
expectation of X 12 Two numbers are selected at random (without replacement) from the first six
positive integers |
1 | 7464-7467 | If X denotes the number of sixes, find the
expectation of X 12 Two numbers are selected at random (without replacement) from the first six
positive integers Let X denote the larger of the two numbers obtained |
1 | 7465-7468 | 12 Two numbers are selected at random (without replacement) from the first six
positive integers Let X denote the larger of the two numbers obtained Find
E(X) |
1 | 7466-7469 | Two numbers are selected at random (without replacement) from the first six
positive integers Let X denote the larger of the two numbers obtained Find
E(X) 13 |
1 | 7467-7470 | Let X denote the larger of the two numbers obtained Find
E(X) 13 Let X denote the sum of the numbers obtained when two fair dice are rolled |
1 | 7468-7471 | Find
E(X) 13 Let X denote the sum of the numbers obtained when two fair dice are rolled Find the variance and standard deviation of X |
1 | 7469-7472 | 13 Let X denote the sum of the numbers obtained when two fair dice are rolled Find the variance and standard deviation of X 14 |
1 | 7470-7473 | Let X denote the sum of the numbers obtained when two fair dice are rolled Find the variance and standard deviation of X 14 A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20,
17, 16, 19 and 20 years |
1 | 7471-7474 | Find the variance and standard deviation of X 14 A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20,
17, 16, 19 and 20 years One student is selected in such a manner that each has
the same chance of being chosen and the age X of the selected student is
recorded |
1 | 7472-7475 | 14 A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20,
17, 16, 19 and 20 years One student is selected in such a manner that each has
the same chance of being chosen and the age X of the selected student is
recorded What is the probability distribution of the random variable X |
1 | 7473-7476 | A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20,
17, 16, 19 and 20 years One student is selected in such a manner that each has
the same chance of being chosen and the age X of the selected student is
recorded What is the probability distribution of the random variable X Find
mean, variance and standard deviation of X |
1 | 7474-7477 | One student is selected in such a manner that each has
the same chance of being chosen and the age X of the selected student is
recorded What is the probability distribution of the random variable X Find
mean, variance and standard deviation of X 15 |
1 | 7475-7478 | What is the probability distribution of the random variable X Find
mean, variance and standard deviation of X 15 In a meeting, 70% of the members favour and 30% oppose a certain proposal |
1 | 7476-7479 | Find
mean, variance and standard deviation of X 15 In a meeting, 70% of the members favour and 30% oppose a certain proposal A member is selected at random and we take X = 0 if he opposed, and X = 1 if
he is in favour |
1 | 7477-7480 | 15 In a meeting, 70% of the members favour and 30% oppose a certain proposal A member is selected at random and we take X = 0 if he opposed, and X = 1 if
he is in favour Find E(X) and Var (X) |
1 | 7478-7481 | In a meeting, 70% of the members favour and 30% oppose a certain proposal A member is selected at random and we take X = 0 if he opposed, and X = 1 if
he is in favour Find E(X) and Var (X) Choose the correct answer in each of the following:
16 |
1 | 7479-7482 | A member is selected at random and we take X = 0 if he opposed, and X = 1 if
he is in favour Find E(X) and Var (X) Choose the correct answer in each of the following:
16 The mean of the numbers obtained on throwing a die having written 1 on three
faces, 2 on two faces and 5 on one face is
(A) 1
(B) 2
(C) 5
(D) 8
3
17 |
1 | 7480-7483 | Find E(X) and Var (X) Choose the correct answer in each of the following:
16 The mean of the numbers obtained on throwing a die having written 1 on three
faces, 2 on two faces and 5 on one face is
(A) 1
(B) 2
(C) 5
(D) 8
3
17 Suppose that two cards are drawn at random from a deck of cards |
1 | 7481-7484 | Choose the correct answer in each of the following:
16 The mean of the numbers obtained on throwing a die having written 1 on three
faces, 2 on two faces and 5 on one face is
(A) 1
(B) 2
(C) 5
(D) 8
3
17 Suppose that two cards are drawn at random from a deck of cards Let X be the
number of aces obtained |
1 | 7482-7485 | The mean of the numbers obtained on throwing a die having written 1 on three
faces, 2 on two faces and 5 on one face is
(A) 1
(B) 2
(C) 5
(D) 8
3
17 Suppose that two cards are drawn at random from a deck of cards Let X be the
number of aces obtained Then the value of E(X) is
(A)
37
221
(B)
135
(C)
131
(D)
2
13
© NCERT
not to be republished
572
MATHEMATICS
13 |
1 | 7483-7486 | Suppose that two cards are drawn at random from a deck of cards Let X be the
number of aces obtained Then the value of E(X) is
(A)
37
221
(B)
135
(C)
131
(D)
2
13
© NCERT
not to be republished
572
MATHEMATICS
13 7 Bernoulli Trials and Binomial Distribution
13 |
1 | 7484-7487 | Let X be the
number of aces obtained Then the value of E(X) is
(A)
37
221
(B)
135
(C)
131
(D)
2
13
© NCERT
not to be republished
572
MATHEMATICS
13 7 Bernoulli Trials and Binomial Distribution
13 7 |
1 | 7485-7488 | Then the value of E(X) is
(A)
37
221
(B)
135
(C)
131
(D)
2
13
© NCERT
not to be republished
572
MATHEMATICS
13 7 Bernoulli Trials and Binomial Distribution
13 7 1 Bernoulli trials
Many experiments are dichotomous in nature |
1 | 7486-7489 | 7 Bernoulli Trials and Binomial Distribution
13 7 1 Bernoulli trials
Many experiments are dichotomous in nature For example, a tossed coin shows a
‘head’ or ‘tail’, a manufactured item can be ‘defective’ or ‘non-defective’, the response
to a question might be ‘yes’ or ‘no’, an egg has ‘hatched’ or ‘not hatched’, the decision
is ‘yes’ or ‘no’ etc |
1 | 7487-7490 | 7 1 Bernoulli trials
Many experiments are dichotomous in nature For example, a tossed coin shows a
‘head’ or ‘tail’, a manufactured item can be ‘defective’ or ‘non-defective’, the response
to a question might be ‘yes’ or ‘no’, an egg has ‘hatched’ or ‘not hatched’, the decision
is ‘yes’ or ‘no’ etc In such cases, it is customary to call one of the outcomes a ‘success’
and the other ‘not success’ or ‘failure’ |
1 | 7488-7491 | 1 Bernoulli trials
Many experiments are dichotomous in nature For example, a tossed coin shows a
‘head’ or ‘tail’, a manufactured item can be ‘defective’ or ‘non-defective’, the response
to a question might be ‘yes’ or ‘no’, an egg has ‘hatched’ or ‘not hatched’, the decision
is ‘yes’ or ‘no’ etc In such cases, it is customary to call one of the outcomes a ‘success’
and the other ‘not success’ or ‘failure’ For example, in tossing a coin, if the occurrence
of the head is considered a success, then occurrence of tail is a failure |
1 | 7489-7492 | For example, a tossed coin shows a
‘head’ or ‘tail’, a manufactured item can be ‘defective’ or ‘non-defective’, the response
to a question might be ‘yes’ or ‘no’, an egg has ‘hatched’ or ‘not hatched’, the decision
is ‘yes’ or ‘no’ etc In such cases, it is customary to call one of the outcomes a ‘success’
and the other ‘not success’ or ‘failure’ For example, in tossing a coin, if the occurrence
of the head is considered a success, then occurrence of tail is a failure Each time we toss a coin or roll a die or perform any other experiment, we call it a
trial |
1 | 7490-7493 | In such cases, it is customary to call one of the outcomes a ‘success’
and the other ‘not success’ or ‘failure’ For example, in tossing a coin, if the occurrence
of the head is considered a success, then occurrence of tail is a failure Each time we toss a coin or roll a die or perform any other experiment, we call it a
trial If a coin is tossed, say, 4 times, the number of trials is 4, each having exactly two
outcomes, namely, success or failure |
1 | 7491-7494 | For example, in tossing a coin, if the occurrence
of the head is considered a success, then occurrence of tail is a failure Each time we toss a coin or roll a die or perform any other experiment, we call it a
trial If a coin is tossed, say, 4 times, the number of trials is 4, each having exactly two
outcomes, namely, success or failure The outcome of any trial is independent of the
outcome of any other trial |
1 | 7492-7495 | Each time we toss a coin or roll a die or perform any other experiment, we call it a
trial If a coin is tossed, say, 4 times, the number of trials is 4, each having exactly two
outcomes, namely, success or failure The outcome of any trial is independent of the
outcome of any other trial In each of such trials, the probability of success or failure
remains constant |
1 | 7493-7496 | If a coin is tossed, say, 4 times, the number of trials is 4, each having exactly two
outcomes, namely, success or failure The outcome of any trial is independent of the
outcome of any other trial In each of such trials, the probability of success or failure
remains constant Such independent trials which have only two outcomes usually
referred as ‘success’ or ‘failure’ are called Bernoulli trials |
1 | 7494-7497 | The outcome of any trial is independent of the
outcome of any other trial In each of such trials, the probability of success or failure
remains constant Such independent trials which have only two outcomes usually
referred as ‘success’ or ‘failure’ are called Bernoulli trials Definition 8 Trials of a random experiment are called Bernoulli trials, if they satisfy
the following conditions :
(i)
There should be a finite number of trials |
1 | 7495-7498 | In each of such trials, the probability of success or failure
remains constant Such independent trials which have only two outcomes usually
referred as ‘success’ or ‘failure’ are called Bernoulli trials Definition 8 Trials of a random experiment are called Bernoulli trials, if they satisfy
the following conditions :
(i)
There should be a finite number of trials (ii)
The trials should be independent |
1 | 7496-7499 | Such independent trials which have only two outcomes usually
referred as ‘success’ or ‘failure’ are called Bernoulli trials Definition 8 Trials of a random experiment are called Bernoulli trials, if they satisfy
the following conditions :
(i)
There should be a finite number of trials (ii)
The trials should be independent (iii)
Each trial has exactly two outcomes : success or failure |
1 | 7497-7500 | Definition 8 Trials of a random experiment are called Bernoulli trials, if they satisfy
the following conditions :
(i)
There should be a finite number of trials (ii)
The trials should be independent (iii)
Each trial has exactly two outcomes : success or failure (iv)
The probability of success remains the same in each trial |
1 | 7498-7501 | (ii)
The trials should be independent (iii)
Each trial has exactly two outcomes : success or failure (iv)
The probability of success remains the same in each trial For example, throwing a die 50 times is a case of 50 Bernoulli trials, in which each
trial results in success (say an even number) or failure (an odd number) and the
probability of success (p) is same for all 50 throws |
1 | 7499-7502 | (iii)
Each trial has exactly two outcomes : success or failure (iv)
The probability of success remains the same in each trial For example, throwing a die 50 times is a case of 50 Bernoulli trials, in which each
trial results in success (say an even number) or failure (an odd number) and the
probability of success (p) is same for all 50 throws Obviously, the successive throws
of the die are independent experiments |
1 | 7500-7503 | (iv)
The probability of success remains the same in each trial For example, throwing a die 50 times is a case of 50 Bernoulli trials, in which each
trial results in success (say an even number) or failure (an odd number) and the
probability of success (p) is same for all 50 throws Obviously, the successive throws
of the die are independent experiments If the die is fair and have six numbers 1 to 6
written on six faces, then p = 1
2 and q = 1 – p = 1
2 = probability of failure |
1 | 7501-7504 | For example, throwing a die 50 times is a case of 50 Bernoulli trials, in which each
trial results in success (say an even number) or failure (an odd number) and the
probability of success (p) is same for all 50 throws Obviously, the successive throws
of the die are independent experiments If the die is fair and have six numbers 1 to 6
written on six faces, then p = 1
2 and q = 1 – p = 1
2 = probability of failure Example 30 Six balls are drawn successively from an urn containing 7 red and 9 black
balls |
1 | 7502-7505 | Obviously, the successive throws
of the die are independent experiments If the die is fair and have six numbers 1 to 6
written on six faces, then p = 1
2 and q = 1 – p = 1
2 = probability of failure Example 30 Six balls are drawn successively from an urn containing 7 red and 9 black
balls Tell whether or not the trials of drawing balls are Bernoulli trials when after each
draw the ball drawn is
(i)
replaced
(ii)
not replaced in the urn |
1 | 7503-7506 | If the die is fair and have six numbers 1 to 6
written on six faces, then p = 1
2 and q = 1 – p = 1
2 = probability of failure Example 30 Six balls are drawn successively from an urn containing 7 red and 9 black
balls Tell whether or not the trials of drawing balls are Bernoulli trials when after each
draw the ball drawn is
(i)
replaced
(ii)
not replaced in the urn Solution
(i)
The number of trials is finite |
1 | 7504-7507 | Example 30 Six balls are drawn successively from an urn containing 7 red and 9 black
balls Tell whether or not the trials of drawing balls are Bernoulli trials when after each
draw the ball drawn is
(i)
replaced
(ii)
not replaced in the urn Solution
(i)
The number of trials is finite When the drawing is done with replacement, the
probability of success (say, red ball) is p = 7
16 which is same for all six trials
(draws) |
1 | 7505-7508 | Tell whether or not the trials of drawing balls are Bernoulli trials when after each
draw the ball drawn is
(i)
replaced
(ii)
not replaced in the urn Solution
(i)
The number of trials is finite When the drawing is done with replacement, the
probability of success (say, red ball) is p = 7
16 which is same for all six trials
(draws) Hence, the drawing of balls with replacements are Bernoulli trials |
1 | 7506-7509 | Solution
(i)
The number of trials is finite When the drawing is done with replacement, the
probability of success (say, red ball) is p = 7
16 which is same for all six trials
(draws) Hence, the drawing of balls with replacements are Bernoulli trials © NCERT
not to be republished
PROBABILITY 573
(ii)
When the drawing is done without replacement, the probability of success
(i |
1 | 7507-7510 | When the drawing is done with replacement, the
probability of success (say, red ball) is p = 7
16 which is same for all six trials
(draws) Hence, the drawing of balls with replacements are Bernoulli trials © NCERT
not to be republished
PROBABILITY 573
(ii)
When the drawing is done without replacement, the probability of success
(i e |
1 | 7508-7511 | Hence, the drawing of balls with replacements are Bernoulli trials © NCERT
not to be republished
PROBABILITY 573
(ii)
When the drawing is done without replacement, the probability of success
(i e , red ball) in first trial is 7
16 , in 2nd trial is 6
15 if the first ball drawn is red or
7
15 if the first ball drawn is black and so on |
1 | 7509-7512 | © NCERT
not to be republished
PROBABILITY 573
(ii)
When the drawing is done without replacement, the probability of success
(i e , red ball) in first trial is 7
16 , in 2nd trial is 6
15 if the first ball drawn is red or
7
15 if the first ball drawn is black and so on Clearly, the probability of success is
not same for all trials, hence the trials are not Bernoulli trials |
1 | 7510-7513 | e , red ball) in first trial is 7
16 , in 2nd trial is 6
15 if the first ball drawn is red or
7
15 if the first ball drawn is black and so on Clearly, the probability of success is
not same for all trials, hence the trials are not Bernoulli trials 13 |
1 | 7511-7514 | , red ball) in first trial is 7
16 , in 2nd trial is 6
15 if the first ball drawn is red or
7
15 if the first ball drawn is black and so on Clearly, the probability of success is
not same for all trials, hence the trials are not Bernoulli trials 13 7 |
1 | 7512-7515 | Clearly, the probability of success is
not same for all trials, hence the trials are not Bernoulli trials 13 7 2 Binomial distribution
Consider the experiment of tossing a coin in which each trial results in success (say,
heads) or failure (tails) |
1 | 7513-7516 | 13 7 2 Binomial distribution
Consider the experiment of tossing a coin in which each trial results in success (say,
heads) or failure (tails) Let S and F denote respectively success and failure in each
trial |
1 | 7514-7517 | 7 2 Binomial distribution
Consider the experiment of tossing a coin in which each trial results in success (say,
heads) or failure (tails) Let S and F denote respectively success and failure in each
trial Suppose we are interested in finding the ways in which we have one success in
six trials |
1 | 7515-7518 | 2 Binomial distribution
Consider the experiment of tossing a coin in which each trial results in success (say,
heads) or failure (tails) Let S and F denote respectively success and failure in each
trial Suppose we are interested in finding the ways in which we have one success in
six trials Clearly, six different cases are there as listed below:
SFFFFF, FSFFFF, FFSFFF, FFFSFF, FFFFSF, FFFFFS |
1 | 7516-7519 | Let S and F denote respectively success and failure in each
trial Suppose we are interested in finding the ways in which we have one success in
six trials Clearly, six different cases are there as listed below:
SFFFFF, FSFFFF, FFSFFF, FFFSFF, FFFFSF, FFFFFS Similarly, two successes and four failures can have
6 |
1 | 7517-7520 | Suppose we are interested in finding the ways in which we have one success in
six trials Clearly, six different cases are there as listed below:
SFFFFF, FSFFFF, FFSFFF, FFFSFF, FFFFSF, FFFFFS Similarly, two successes and four failures can have
6 4 |
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