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प्रश्न
Bernoulli distribution is a particular case of binomial distribution if n = ______
विकल्प
4
10
2
1
उत्तर
1
संबंधित प्रश्न
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?
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.
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
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 8 times. Find the probability that it shows heads exactly 5 times.
A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.
If getting 5 or 6 in a throw of an unbiased die is a success and the random variable X denotes the number of successes in six throws of the die, find P (X ≥ 4).
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 ?
A box contains 100 tickets, each bearing one of the numbers from 1 to 100. If 5 tickets are drawn successively with replacement from the box, find the probability that all the tickets bear numbers divisible by 10.
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 none will fuse after 150 days of use
Find the probability distribution of the number of sixes in three tosses of a die.
A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.
An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of successes.
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.
Five dice are thrown simultaneously. If the occurrence of 3, 4 or 5 in a single die is considered a success, find the probability of at least 3 successes.
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.
Six coins are tossed simultaneously. Find the probability of getting
(i) 3 heads
(ii) no heads
(iii) at least one head
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.
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.
Suppose X has a binomial distribution with n = 6 and \[p = \frac{1}{2} .\] Show that X = 3 is the most likely outcome.
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.
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.
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.
Find the probability that in 10 throws of a fair die, a score which is a multiple of 3 will be obtained in at least 8 of the throws.
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 exactly two bulbs are 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
Can the mean of a binomial distribution be less than its variance?
If the mean and variance of a binomial distribution are respectively 9 and 6, find the distribution.
Find the binomial distribution when the sum of its mean and variance for 5 trials is 4.8.
Determine the binomial distribution whose mean is 20 and variance 16.
The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial distribution.
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.
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.
The probability that an item produced by a factory is defective is 0.02. A shipment of 10,000 items is sent to its warehouse. Find the expected number of defective items and the standard deviation.
If X follows a binomial distribution with mean 4 and variance 2, find P (X ≥ 5).
If the sum of the mean and variance of a binomial distribution for 6 trials is \[\frac{10}{3},\] find the distribution.
A die is tossed twice. A 'success' is getting an even number on a toss. Find the variance of number of successes.
If in a binomial distribution mean is 5 and variance is 4, write the number of trials.
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 binomial variate X are 2 and 1 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.
In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?
A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire in order to have more than 50% chance of hitting it at least once is
A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads is
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
Let X denote the number of times heads occur in n tosses of a fair coin. If P (X = 4), P (X= 5) and P (X = 6) are in AP, the value of n is
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
The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, 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 = 100 and p = 1/3, then P (X = r) is maximum when r =
A fair die is tossed eight times. The probability that a third six is observed in the eighth throw 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 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:
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 all are white ?
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 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
For Bernoulli Distribution, state formula for E(X) and V(X).
If x4 occurs in the tth term in the expansion of `(x^4 + 1/x^3)^15`, then the value oft is equal to:
If the coefficients of x7 and x8 in `(2 + x/3)^n` are equal, then n is
A pair of dice is thrown four times. If getting a doublet is considered a success then find the probability of two success.
A box B1 contains 1 white ball and 3 red balls. Another box B2 contains 2 white balls and 3 red balls. If one ball is drawn at random from each of the boxes B1 and B2, then find the probability that the two balls drawn are of the same colour.
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 the sum of mean and variance of a binomial distribution is `25/9` for 5 trials, find p.
If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.
An experiment succeeds thrice as often as it fails. Then in next five trials, find the probability that there will be two successes.
For the binomial distribution X ∼ B(n, p), n = 6 and P(X = 4) = P(X = 2). find p.
