Advertisements
Advertisements
प्रश्न
A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.
Advertisements
उत्तर
Let X = no. of heads shows
n = 9 p = `1/2` q = `1/2`
P(X = x) = `""^nC_x p^n.(q)^(n-x)` X = 0,1.....n
P(X = 5) = `""^9C_5 (1/2)^5(1/2)^4`
`= (9xx8xx7xx6)/(4xx3xx2xx1) xx 1/2^9`
`= 3024/24 xx 1/2^9`
`= 126/2^9`
`= 126/512`
= 0.2460
APPEARS IN
संबंधित प्रश्न
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one, will fuse after 150 days of use.
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
(A) 10−1
(B) `(1/2)^5`
(C) `(9/10)^5`
(D) 9/10
The probability that a student is not a swimmer is 1/5 . Then the probability that out of five students, four are swimmers is
(A) `""^5C_4 (4/5)^4 1/5`
(B) `(4/5)^4 1/5
(C) `""^5C_1 1/5 (4/5)^4 `
(D) None of these
In a large bulk of items, 5 percent of the items are defective. What is the probability that a sample of 10 items will include not more than one defective item?
A bag contains 7 green, 4 white and 5 red balls. If four balls are drawn one by one with replacement, what is the probability that one is red?
A card is drawn and replaced in an ordinary pack of 52 cards. How many times must a card be drawn so that (i) there is at least an even chance of drawing a heart (ii) the probability of drawing a heart is greater than 3/4?
An unbiased coin is tossed 8 times. Find, by using binomial distribution, the probability of getting at least 6 heads.
In a hospital, there are 20 kidney dialysis machines and the chance of any one of them to be out of service during a day is 0.02. Determine the probability that exactly 3 machines will be out of service on the same day.
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university none will graduate
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university only one will graduate .
The probability of a shooter hitting a target is \[\frac{3}{4} .\] How many minimum number of times must he/she fire so that the probability of hitting the target at least once is more than 0.99?
How many times must a man toss a fair coin so that the probability of having at least one head is more than 80% ?
A factory produces bulbs. The probability that one bulb is defective is \[\frac{1}{50}\] and they are packed in boxes of 10. From a single box, find the probability that none of the bulbs is defective .
A factory produces bulbs. The probability that one bulb is defective is \[\frac{1}{50}\] and they are packed in boxes of 10. From a single box, find the probability that more than 8 bulbs work properly
If the mean and variance of a binomial distribution are respectively 9 and 6, find the distribution.
If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P (X ≤ 5).
If X follows a binomial distribution with mean 4 and variance 2, find P (X ≥ 5).
The mean and variance of a binomial distribution are \[\frac{4}{3}\] and \[\frac{8}{9}\] respectively. Find P (X ≥ 1).
A die is tossed twice. A 'success' is getting an even number on a toss. Find the variance of number of successes.
A die is thrown three times. Let X be 'the number of twos seen'. Find the expectation of X.
In a group of 200 items, if the probability of getting a defective item is 0.2, write the mean of the distribution.
If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X = 4) in terms of α.
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.
If X is a binomial variate with parameters n and p, where 0 < p < 1 such that \[\frac{P\left( X = r \right)}{P\left( X = n - r \right)}\text{ is } \] independent of n and r, then p equals
A fair coin is tossed 99 times. If X is the number of times head appears, then P (X = r) is maximum when r is
If X follows a binomial distribution with parameters n = 8 and p = 1/2, then P (|X − 4| ≤ 2) equals
Mark the correct alternative in the following question:
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If \[\frac{P\left( X = r \right)}{P\left( X = n - r \right)}\] is independent of n and r, then p equals
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that none is a spade ?
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs at least one will fuse after 150 days of use
Determine the binomial distribution where mean is 9 and standard deviation is `3/2` Also, find the probability of obtaining at most one success.
Find the mean and variance of the random variable X which denotes the number of doublets in four throws of a pair of dice.
Bernoulli distribution is a particular case of binomial distribution if n = ______
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If P(x = r)/P(x = n – r) is independent of n and r, then p equals ______.
If in the binomial expansion of (1 + x)n where n is a natural number, the coefficients of the 5th, 6th and 7th terms are in A.P., then n is equal to:
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is:-
The mean and variance of a binomial distribution are α and `α/3` respectively. If P(X = 1) = `4/243`, then P(X = 4 or 5) is equal to ______.
An experiment succeeds thrice as often as it fails. Then in next five trials, find the probability that there will be two successes.
