Advertisements
Advertisements
प्रश्न
It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week.
Advertisements
उत्तर
Let X = number of days it rains in a week.
p = probability that it rains
∴ p = `12/30 = 2/5`
and q = 1 - p = `1 - 2/5 = 3/5`
Given: n = 7
∴ X ~ B `(7, 2/5)`
The p.m.f. of X is given by
P(X = x) = `"^nC_x p^x q^(n - x)`
i.e. p(x) = `"^7C_x (2/5)^x (3/5)^(7 - x)` x = 0, 1, 2, ...., 7
P(it rains exactly 3 days of week) = P(X = 3)
= p(3) = `"^7C_3 (2/5)^3 (3/5)^(7 - 3)`
`= (7 xx 6 xx 5)/(3 xx 2 xx 1) (8/125)(81/625)`
`= 35(8/125)(81/625) = (35 xx 8 xx 81)/5^7`
`= 22680/78125 = 0.2903`
Hence, the probability that it rains exactly 3 days of week = `35 xx 8 xx 81/5^7` OR 0.2903.
APPEARS IN
संबंधित प्रश्न
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
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 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?
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 ≤ 8).
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.
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.
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 Binomial distribution if n is very large and probability success of p is very small such that np = m (constant) then _______ distribution is applied.
Choose the correct alternative:
A sequence of dichotomous experiments is called a sequence of Bernoulli trials if it satisfies ______
In Binomial distribution, probability of success ______ from trial to trial
State whether the following statement is True or False:
For the Binomial distribution, Mean E(X) = m and Variance = Var(X) = m
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 = ______.
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
