Advertisements
Advertisements
प्रश्न
If X follows a binomial distribution with parameters n = 8 and p = 1/2, then P (|X − 4| ≤ 2) equals
पर्याय
\[\frac{118}{128}\]
\[\frac{119}{128}\]
\[\frac{117}{128}\]
None Of these
उत्तर
\[\frac{119}{128}\]
\[n = 8, p = \frac{1}{2}\]
\[ \therefore q = 1 - \frac{1}{2} = \frac{1}{2}\]
\[\text{ Hence, the distribution is given by } \]
\[P(X = r) =^{8}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{8 - r} \]
\[P\left( \left| X - 4 \right| \right) \leq 2 \]
\[ = P( - 2 \leq X - 4 \leq 2) \]
\[ = P(2 \leq X \leq 6)\]
\[ = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)\]
\[ = \frac{^{8}{}{C}_2 + ^{8}{}{C}_3 + ^{8}{}{C}_4 + ^{8}{}{C}_5 + ^{8}{}{C}_6}{2^8}\]
\[ = \frac{28 + 56 + 70 + 56 + 28}{256}\]
\[ = \frac{238}{256}\]
\[ = \frac{119}{128}\]
APPEARS IN
संबंधित प्रश्न
Given X ~ B (n, p)
If n = 10 and p = 0.4, find E(X) and var (X).
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.
The probability of a man hitting a target is 1/4. If he fires 7 times, what is the probability of his hitting the target at least twice?
A bag contains 10 balls, each marked with one of the digits from 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?
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 mathematics department has 8 graduate assistants who are assigned to the same office. Each assistant is just as likely to study at home as in office. How many desks must there be in the office so that each assistant has a desk at least 90% of the time?
It is known that 60% of mice inoculated with a serum are protected from a certain disease. If 5 mice are inoculated, find the probability that more than 3 contract the disease .
An experiment succeeds twice as often as it fails. Find the probability that in the next 6 trials there will be at least 4 successes.
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 person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is \[\frac{1}{100} .\] What is the probability that he will win a prize at least twice.
From a lot of 30 bulbs that includes 6 defective bulbs, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
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
Can the mean of a binomial distribution be less than its variance?
The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial distribution.
The mean and variance of a binomial variate with parameters n and p are 16 and 8, respectively. Find P (X = 0), P (X = 1) and P (X ≥ 2).
In eight throws of a die, 5 or 6 is considered a success. Find the mean number of successes and the standard deviation.
Find the expected number of boys in a family with 8 children, assuming the sex distribution to be equally probable.
If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P (X ≤ 5).
If in a binomial distribution mean is 5 and variance is 4, write the number of trials.
If in a binomial distribution n = 4, P (X = 0) = \[\frac{16}{81}\], then P (X = 4) equals
A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears is
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
One hundred identical coins, each with probability p of showing heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is
A fair die is tossed eight times. The probability that a third six is observed in the eighth throw is
A five-digit number is written down at random. The probability that the number is divisible by 5, and no two consecutive digits are identical, is
A coin is tossed 10 times. The probability of getting exactly six heads is
If the mean and variance of a binomial distribution are 4 and 3, respectively, the probability of getting exactly six successes in this distribution is
The probability of selecting a male or a female is same. If the probability that in an office of n persons (n − 1) males being selected is \[\frac{3}{2^{10}}\] , the value of n is
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?
A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that any two are white ?
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
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:
A student is given a quiz with 10 true or false questions and he answers by sheer guessing. If X is the number of questions answered correctly write the p.m.f. of X. If the student passes the quiz by getting 7 or more correct answers what is the probability that the student passes the quiz?
A fair coin is tossed 6 times. Find the probability of getting heads 4 times.
If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.
