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प्रश्न
Bernoulli distribution is a particular case of binomial distribution if n = ______
पर्याय
4
10
2
1
उत्तर
1
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 pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
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?
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’; if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.
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)
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?
Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?
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 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?
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.
A fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times.
Assume that on an average one telephone number out of 15 called between 2 P.M. and 3 P.M. on week days is busy. What is the probability that if six randomly selected telephone numbers are called, at least 3 of them will be busy?
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 ?
Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?
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.
A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.
A man wins a rupee for head and loses a rupee for tail when a coin is tossed. Suppose that he tosses once and quits if he wins but tries once more if he loses on the first toss. Find the probability distribution of the number of rupees the man wins.
The items produced by a company contain 10% defective items. Show that the probability of getting 2 defective items in a sample of 8 items is
\[\frac{28 \times 9^6}{{10}^8} .\]
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?
Six coins are tossed simultaneously. Find the probability of getting
(i) 3 heads
(ii) no heads
(iii) at least one head
Suppose that a radio tube inserted into a certain type of set has probability 0.2 of functioning more than 500 hours. If we test 4 tubes at random what is the probability that exactly three of these tubes function for more than 500 hours?
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 .
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 .
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 at least 2 will strike the target
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 .
Ten eggs are drawn successively, with replacement, from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.
In a 20-question true-false examination, suppose a student tosses a fair coin to determine his answer to each question. For every head, he answers 'true' and for every tail, he answers 'false'. Find the probability that he answers at least 12 questions correctly.
Suppose X has a binomial distribution with n = 6 and \[p = \frac{1}{2} .\] Show that X = 3 is the most likely outcome.
In a multiple-choice examination with three possible answers for each of the five questions out of which only one is correct, what is the probability that a candidate would get four or more correct answers just by guessing?
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 win a prize at least once.
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 exactly once.
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.
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 90% ?
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 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 .
If the probability of a defective bolt is 0.1, find the (i) mean and (ii) standard deviation for the distribution of bolts in a total of 400 bolts.
If on an average 9 ships out of 10 arrive safely at ports, find the mean and S.D. of the ships returning safely out of a total of 500 ships.
A dice is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of successes.
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.
In a binomial distribution, if n = 20 and q = 0.75, then write its mean.
If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.
If the mean and variance of a binomial variate X are 2 and 1 respectively, find P (X > 1).
If in a binomial distribution n = 4 and P (X = 0) = \[\frac{16}{81}\] , find q.
If the mean and variance of a binomial distribution are 4 and 3, respectively, find the probability of no success.
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.
In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?
If in a binomial distribution n = 4, P (X = 0) = \[\frac{16}{81}\], then P (X = 4) equals
A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
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
If X follows a binomial distribution with parameters n = 8 and p = 1/2, then P (|X − 4| ≤ 2) equals
A fair die is tossed eight times. The probability that a third six is observed in the eighth throw is
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
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
In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean is
A coin is tossed 4 times. The probability that at least one head turns up is
For a binomial variate X, if n = 3 and P (X = 1) = 8 P (X = 3), then p =
A coin is tossed n times. The probability of getting at least once is greater than 0.8. Then, the least 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
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 only 3 cards are spades ?
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 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.
For Bernoulli Distribution, state formula for E(X) and V(X).
For X ~ B(n, p) and P(X = x) = `""^8"C"_x(1/2)^x (1/2)^(8 - x)`, then state value of n and p
The mean, median and mode for binomial distribution will be equal when
The sum of n terms of the series `1 + 2(1 + 1/n) + 3(1 + 1/n)^2 + ...` is
If the coefficients of x7 and x8 in `(2 + x/3)^n` are equal, then n 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 (33, p) such that 3P(X = 0) = P(X = 1), then the value of `(P(X = 15))/(P(X = 18)) - (P(X = 16))/(P(X = 17))` 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 8 times. Find the probability that it shows heads at most once.
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.
The mean and variance of binomial distribution are 4 and 2 respectively. Find the probability of two successes.
