Advertisements
Advertisements
प्रश्न
In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly one floppy disc work.
Advertisements
उत्तर
Let X = number of working discs.
p = probability that a floppy disc works
∴ p = 95% = `95/100 = 19/20`
and q = 1 - p = `1 - 19/20 = 1/20`
Given: n = 3
∴ X ~ B`(3, 19/20)`
The p.m.f. of X is given by
P(X = x) = `"^nC_x p^x q^(n - x)`
i.e. p(x) = `"^3C_x (19/20)^x (1/20)^(3-x)`, x = 0, 1, 2, 3
P(exactly one floppy discs work) = P(X = 1)
= p(1) = `"^3C_1 (19/20)^1 (1/20)^(3 - 1)`
`= 3 xx 19/20 xx (1/20)^2`
`= 3(19/20^3)`
Hence, the probability that none of the floppy disc will work = 3`(19/20^3)`
APPEARS IN
संबंधित प्रश्न
The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly two of the next four components tested will survive.
A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of 5 successes.
A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at least 5 successes.
A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at most 5 successes.
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; find the probability that all the five cards are spades.
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards; find the probability that none is a spade.
In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly two floppy disc work.
In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that all 3 of the sample will work.
Choose the correct option from the given alternatives:
A die is thrown 100 times. If getting an even number is considered a success, then the standard deviation of the number of successes is ______.
Choose the correct option from the given alternatives:
The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
Choose the correct option from the given alternatives:
For a binomial distribution, n = 5. If P(X = 4) = P(X = 3), then p = ______
For a binomial distribution, n = 4. If 2P(X = 3) = 3P(X = 2), then p = ______.
If X ~ B(4, p) and P(X = 0) = `16/81`, then P(X = 4) = ______.
Choose the correct option from the given alternatives:
The probability of a shooter hitting a target is `3/4` How many minimum numbers of times must he fire so that the probability of hitting the target at least once is more than 0·99?
Let X ~ B(10, 0.2). Find P(X = 1).
Let X ~ B(10, 0.2). Find P(X ≥ 1).
Let X ~ B(10, 0.2). Find P(X ≤ 8).
The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 2 will miss the target.
The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: at most three have a burst tyre
A large chain retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 3%. The inspector of the retailer picks 20 items from a shipment. What is the probability that the store will receive at most one defective item?
An examination consists of 10 multiple choice questions, in each of which a candidate has to deduce which one of five suggested answers is correct. A completely unprepared student guesses each answer completely randomly. What is the probability that this student gets 8 or more questions correct? Draw the appropriate morals.
The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that all 8 machines.
A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 0.
A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 1.
A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 3 or more, terminals will require attention during the next week.
It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week.
If E(x) > Var(x) then X follows _______.
In Binomial distribution if n is very large and probability success of p is very small such that np = m (constant) then _______ distribution is applied.
In a Binomial distribution with n = 4, if 2P(X = 3) = 3P(X = 2), then value of p is ______.
If X ~ B(n, p) with n = 10, p = 0.4, then find E(X2).
Choose the correct alternative:
A sequence of dichotomous experiments is called a sequence of Bernoulli trials if it satisfies ______
If X follows a binomial distribution with parameters n = 10 and p. If 4P(X = 6) = P(X = 4), then p = ______
In a binomial distribution `B(n, p = 1/4)`, if the probability of at least one success is greater than or equal to `9/10`, then n is greater than ______.
In a binomial distribution `B(n, p = 1/4)`, if the probability of at least one success is greater than or equal to `9/10`, then n is greater than ______.
If X∼B (n, p) with n = 10, p = 0.4 then E(X2) = ______.
In a binomial distribution, n = 4 and 2P(X = 3) = 3P(X = 2), then q = ______.
