Advertisements
Advertisements
प्रश्न
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 7 or 8 machines.
Advertisements
उत्तर
Let X = number of machines that produce the bolts within specification.
p = probability that a machine produce bolts within specification
p = 0.998
and q = 1 - p = 1 - 0.998 = 0.002
Given: n = 8
∴ X ~ B (8, 0.998)
The p.m.f. of X is given by
P(X = x) = `"^nC_x p^x q^(n - x)`
i.e. p(x) = `"^8C_x (0.998)^x (0.002)^(8 - x)`, x = 0, 1, 2,...,8
P(7 or 8 machines will produce all bolts within specification) = P(X = 7) + P(X = 8)
`= ""^8C_7 (0.998)^7 (0.002)^(8 -7) + "^8C_8 (0.998)^8 (0.002)^(8 -8)`
`= 8 xx (0.998)^7 (0.002)^1 + 1xx (0.998)^8 (0.002)^0`
`= (0.998)^7 [8(0.002) + 0.998]`
`= (0.016 + 0.998)(0.998)^7`
`= (1.014) xx (0.998)^7`
Hence, the probability that 7 or 8 machines produce all bolts within specification = `(1.014) xx (0.998)^7`
APPEARS IN
संबंधित प्रश्न
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.
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 only 3 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 none of the 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 exactly one 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 exactly two floppy disc 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).
A lot of 100 items contain 10 defective items. Five items are selected at random from the lot and sent to the retail store. What is the probability that the store will receive at most one defective item?
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?
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.
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 at most 6 machines will produce all bolts within specification.
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 2.
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.
In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.
Calculate the probabilities of obtaining an answer yes from 0, 1, 2, 3, 4 of the pupils.
In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.
Find the probability that the visitor obtains answer yes from at least 2 pupils:
- when the number of pupils questioned remains at 4.
- when the number of pupils questioned is increased to 8.
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 the probability of success in a single trial is 0.01. How many trials are required in order to have a probability greater than 0.5 of getting at least one success?
If E(x) > Var(x) then X follows _______.
If X ~ B(n, p) with n = 10, p = 0.4, then find E(X2).
State whether the following statement is True or False:
For the Binomial distribution, Mean E(X) = m and Variance = Var(X) = m
If the sum of the mean and the variance of a binomial distribution for 5 trials Is 1.8, then p = ______.
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 = ______.
A pair of dice is thrown 3 times. If getting a doublet is considered a success, find the probability of getting at least two success.
Solution:
A pair of dice is thrown 3 times.
∴ n = 3
Let x = number of success (doublets)
p = probability of success (doublets)
∴ p = `square`, q = `square`
∴ x ∼ B (n, p)
P(x) = nCxpx qn–x
Probability of getting at least two success means x ≥ 2.
∴ P(x ≥ 2) = P(x = 2) + P(x = 3)
= `square` + `square`
= `2/27`
