Advertisements
Advertisements
प्रश्न
An unbiased coin is tossed 8 times. Find, by using binomial distribution, the probability of getting at least 6 heads.
उत्तर
Let X be the number of heads in tossing the coin 8 times.
X follows a binomial distribution with n = 8
\[p = \frac{1}{2} \text{ and q } = \frac{1}{2}\]
\[\text{ Hence, the distribution is given by } \]
\[ \therefore P(X = r) = ^{8}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{8 - r} , r = 0, 1, 2, 3, 4, 5, 6, 7, 8\]
\[\text{ Required probability } = P(X \geq 6)\]
\[ = P(X = 6) + P(X = 7) + P(X = 8)\]
\[ = \frac{^{8}{}{C}_6 + ^{8}{}{C}_7 + ^{8}{}{C}_8}{2^8}\]
\[ = \frac{28 + 8 + 1}{256}\]
\[ = \frac{37}{256}\]
APPEARS IN
संबंधित प्रश्न
The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 4 will hit the target.
Given X ~ B (n, p)
If n = 10 and p = 0.4, find E(X) and var (X).
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100. What is the probability that he will in a prize (a) at least once (b) exactly once (c) at least twice?
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
Five cards are drawn one by one, with replacement, from a well-shuffled deck of 52 cards. Find the probability that
(i) all the five cards diamonds
(ii) only 3 cards are diamonds
(iii) none is a diamond
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that all the five cards are spades ?
An urn contains four white and three red balls. Find the probability distribution of the number of red balls in three draws with replacement from the urn.
The probability that a certain kind of component will survive a given shock test is \[\frac{3}{4} .\] Find the probability that among 5 components tested at most 3 will survive .
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 .
A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
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 box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.
In a group of 200 items, if the probability of getting a defective item is 0.2, write the mean of the distribution.
If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.
The mean of a binomial distribution is 10 and its standard deviation is 2; write the value of q.
If the mean and variance of a random variable X with a binomial distribution are 4 and 2 respectively, find P (X = 1).
If the mean and variance of a binomial distribution are 4 and 3, respectively, find the probability of no success.
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.
A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is
If X follows a binomial distribution with parameters n = 8 and p = 1/2, then P (|X − 4| ≤ 2) equals
For a binomial variate X, if n = 3 and P (X = 1) = 8 P (X = 3), then p =
Mark the correct alternative in the following question:
A box contains 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?
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
Mark the correct alternative in the following question:
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is
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
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 ______.
The mean, median and mode for binomial distribution will be equal when
For the binomial distribution X ∼ B(n, p), n = 6 and P(X = 4) = P(X = 2). find p.
