Advertisements
Advertisements
Question
Suppose X has a binomial distribution `B(6, 1/2)`. Show that X = 3 is the most likely outcome.
(Hint: P(X = 3) is the maximum among all P (xi), xi = 0, 1, 2, 3, 4, 5, 6)
Solution
X is the random variable whose binomial distribution is `B(6, 1/2)`..
Therefore, n = 6 and p = 1/2
The value of `""^6C_3` is maximum. Therefore, for x = 3, P(X = x) is maximum.
Thus, X = 3 is the most likely outcome.
APPEARS IN
RELATED QUESTIONS
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that
- all the five cards are spades?
- only 3 cards are spades?
- none is a spade?
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.
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?
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6 . What is the probability that he will knock down fewer than 2 hurdles?
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.
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
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 none is white ?
A bag contains 2 white, 3 red and 4 blue balls. Two balls are drawn at random from the bag. If X denotes the number of white balls among the two balls drawn, describe the probability distribution of X.
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.
Assume that the probability that a bomb dropped from an aeroplane will strike a certain target is 0.2. If 6 bombs are dropped, find the probability that exactly 2 will strike the target .
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes.
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 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 X follows a binomial distribution with mean 4 and variance 2, find P (X ≥ 5).
A die is thrown three times. Let X be 'the number of twos seen'. Find the expectation of X.
If in a binomial distribution n = 4 and P (X = 0) = \[\frac{16}{81}\] , find q.
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
Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 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:
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
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 not more than one will fuse after 150 days of use
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 more than one will fuse after 150 days of use
Explain why the experiment of tossing a coin three times is said to have binomial distribution.
The sum of n terms of the series `1 + 2(1 + 1/n) + 3(1 + 1/n)^2 + ...` is
If a fair coin is tossed 10 times. Find the probability of getting at most six heads.
If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then `(P(X = 2))/(P(X = 3))` is equal to ______.
In three throws with a pair of dice find the chance of throwing doublets at least twice.
A fair coin is tossed 6 times. Find the probability of getting heads 4 times.
The mean and variance of binomial distribution are 4 and 2 respectively. Find the probability of two successes.
