Advertisements
Advertisements
प्रश्न
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?
उत्तर
Let p be the probability of success that people are right-handed
⇒ `p = 90/100 = 9/10`
and `q = 1 - p = 1 - 9/10 = 1/10`
∴ X has a binomial distribution with
`n = 10, p = 9/10, q = 1/10`
∴ P (X = r) = nCr (q)n-r pr
Required probability = P(at most 6 of 10 people are right-handed)
= P (X ≤ 6) = 1 - P (7 ≤ X ≤ 10)
`= 1 - sum_(r =17)^10 ""^10C_r (9/10)^r (1/10)^(10-r)`
`= 1- sum_(r=7)^10 ""^10C_r (0.9)^r (0.1)^(10-r)`
APPEARS IN
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
It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?
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 large bulk of items, 5 percent of the items are defective. What is the probability that a sample of 10 items will include not more than one defective item?
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
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?
Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the mean and variance of number of red cards.
An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of successes.
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?
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 none 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 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 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 .
The mean and variance of a binomial distribution are \[\frac{4}{3}\] and \[\frac{8}{9}\] respectively. Find P (X ≥ 1).
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 n = 4, P (X = 0) = \[\frac{16}{81}\], then P (X = 4) equals
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
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
For a binomial variate X, if n = 3 and P (X = 1) = 8 P (X = 3), then p =
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that none is a spade ?
Explain why the experiment of tossing a coin three times is said to have binomial distribution.
Which one is not a requirement of a binomial distribution?
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If P(x = r)/P(x = n – r) is independent of n and r, then p equals ______.
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
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.
The probability of hitting a target in any shot is 0.2. If 5 shots are fired, find the probability that the target will be hit at least twice.
In three throws with a pair of dice find the chance of throwing doublets at least twice.
An experiment succeeds thrice as often as it fails. Then in next five trials, find the probability that there will be two successes.
