Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Let X = number of defective items.
p = probability that item is defective
∴ p = `10/100 = 1/10`
∴ q = `1 - "p" = 1 - 1/10 = 9/10`
Given: n = 5
∴ X ~ B `(5, 1/10)`
The p.m.f. of X is given as:
P[X = x] = `"^nC_x p^x q^(n - x)`
i.e. p(x) = `"^5C_x (1/10)^x (9/10)^(5 - x)`
P (store will receive at most one defective item)
= P[X ≤ 1] = P[X = 0] + P[X = 1]
= p(0) + p(1)
`= ""^5C_0 (1/10)^0 (9/10)^(5 - 0) + "^5C_1 (1/10)^1 (9/10)^(5 - 1)`
`= 1 xx 1 xx (9/10)^5 + 5 xx 1/10 xx (9/10)^4`
`= (0.9)^5 + (0.05)(0.9)^4`
`= (0.9 + 0.5)(0.9)^4`
= (1.4)(0.9)4
Hence, the probability that the store will receive at most one defective item is (1.4)(0.9)4
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.
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 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 ______.
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) = ______.
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
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.
The probability that a lamp in a classroom will be burnt out is 0.3. Six such lamps are fitted in the class-room. If it is known that the classroom is unusable if the number of lamps burning in it is less than four, find the probability that the classroom cannot be used on a random occasion.
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.
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 it will rain at least 2 days of a given 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?
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.
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 = ______.
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`
If X is a binomial variable with range {0, 1, 2, 3, 4} and P(X = 3) = 3P(X = 4) then the parameter ‘p’ of the binomial distribution is
