Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Let X = number of defective items
p = probability of defective item
∴ p = 5% = `5/100 = 1/20`
and q = 1 – p = `1 - 1/20 = 19/20`
∴ `X ~ B (10, 1/20)`
The p.m.f. of X is given by
P(X = x) = `"^nC_x p^x q^(n - x)`
i.e. p(x) = `"^10C_x (1/20)^x (19/20)^(10 - x)`, x = 0, 1, 2, ..., 10
P(sample of 10 items will include not more than one defective item) = P[X ≤ 1]
= P(X = 0) + P(X = 1)
= `""^10C_0 (1/20)^0(19/20)^(10 - 0) + "^10C_1 (1/20)^1 (19/20)^(10 - 1)`
= `1*1*(19/20)^10 + 10 xx (1/20) xx (19/20)^9`
= `(19/20)^9 [19/20 + 10/20]`
= `(19/20)^9 (29/20)`
= `29(19^9/20^10)`
Hence, the probability that a sample of 10 items will include not more than one defective item = `29 (19^9/20^10)`.
संबंधित प्रश्न
Given that X ~ B(n= 10, p). If E(X) = 8 then the value of
p is ...........
(a) 0.6
(b) 0.7
(c) 0.8
(d) 0.4
A fair coin is tossed 8 times. Find the probability that it shows heads at least once
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.
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?
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.
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
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?
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?
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.
Six coins are tossed simultaneously. Find the probability of getting
(i) 3 heads
(ii) no heads
(iii) at least one head
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 none contract the disease .
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.
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 twice.
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90% ?
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 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 exactly two bulbs are defective
Determine the binomial distribution whose mean is 20 and variance 16.
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).
In a binomial distribution, if n = 20 and q = 0.75, then write its mean.
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
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
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 =
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:
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is
Mark the correct alternative in the following question:
Which one is not a requirement of a binomial dstribution?
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
Find the mean and variance of the random variable X which denotes the number of doublets in four throws of a pair of dice.
The mean, median and mode for binomial distribution will be equal when
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.
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 ______.
The mean and variance of binomial distribution are 4 and 2 respectively. Find the probability of two successes.
