Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Let X = number of a defective electronic device.
p = probability that a device is defective
∴ p = 3% = `3/100`
∴ q = 1 - p = `1 - 3/100 = 97/100`
Given: n = 20
∴ X ~ B `(20, 3/100)`
The p.m.f. of X is given as :
P[X = x] = `"^nC_x p^x q^(n - x)`
i.e. p(x) = `"^20C_x (3/100)^x (97/100)^(20 - x)`
P (store will receive at most one defective item)
= P[X ≤ 1] = p[X = 0] + P[X = 1]
= p(0) + p(1)
`= ""^20C_0 (3/100)^0 (97/100)^(20 - 0) + "^20C_1 (3/100)^1 (97/100)^(20 - 1)`
`= 1 xx 1 xx (0.97)^20 + 20xx (0.03) xx (0.97)^19`
`= (0.97 + 0.6)(0.97)^19`
`= (1.57)(0.97)^19`
Hence, the probability that the store will receive at most one defective item `= (1.57)(0.97)^19`
[Note: Answer in the textbook is incorrect.]
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 at most 5 successes.
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 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:
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) = ______.
If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ______.
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: exactly one has a burst tyre
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
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: two or more have burst tyre.
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 at most 6 machines will produce all bolts within specification.
The probability that a machine develops a fault within the first 3 years of use is 0.003. If 40 machines are selected at random, calculate the probability that 38 or more will not develop any faults within the first 3 years of use.
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 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.
In binomial distribution with five Bernoulli’s trials, the probability of one and two success are 0.4096 and 0.2048 respectively. Find the probability of success.
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.
Solve the following problem:
An examination consists of 5 multiple choice questions, in each of which the candidate has to decide which one of 4 suggested answers is correct. A completely unprepared student guesses each answer completely randomly. Find the probability that,
- the student gets 4 or more correct answers.
- the student gets less than 4 correct answers.
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).
In Binomial distribution, probability of success ______ from trial to trial
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 ______.
