Advertisements
Advertisements
प्रश्न
Let X ~ B(10, 0.2). Find P(X ≤ 8).
उत्तर
X ~ B(10, 0.2)
∴ n = 10, p = 0.2
∴ q = 1 - p = 1 - 0.2 = 0.8
The p,m.f. of X is given by
P(X = x) = `"^nC_x p^x q^(n - x)`
∴ P(X = x) = `"^10C_x (0.2)^x (0.8)^(10 - x)`, x = 0, 1, 2, 3,....,10
P(X ≤ 8) = 1 - P(X > 8)
= 1 - [P(X = 9) + P(X = 10)]
`= 1 - [""^10C_9 (0.2)^9 (0.8)^(10 - 9) + "^10C_10 (0.2)^10 (0.8)^(10-10)]`
`= 1 - [10 (0.2)^9 (0.8)^1 + 1(0.2)^10 (0.8)^0]`
`= 1 - (0.2)^9 [10(0.8) + (0.2)]`
`= 1 - (0.2)^9 [8 + 0.2]`
`= 1 - (8.2)(0.2)^9`
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.
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards, find the probability that only 3 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 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 ______.
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).
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?
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 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.
It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week.
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 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 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 ______.
In Binomial distribution, probability of success ______ from trial to trial
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 ______.
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`
