Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let X = number of pupils like Mathematics.
p = probability that pupils like Mathematics
∴ p = 80% = `80/100 = 4/5`
and q = 1 - p = `1 - 4/5 = 1/5`
Given: n = 4
∴ X ~ B `(4, 4/5)`
The p.m.f. of X is given by
P(X = x) = `"^nC_x p^x q^(n - x)`
i.e. p(x) = `"^4C_x (4/5)^x (1/5)^(4 - x)` x = 0, 1, 2, 3, 4
The probabilities of obtaining an answer yes from 0, 1, 2, 3, 4 of pupils are P(X= 0), P(X = 1), P(X = 2), P(X = 3) and P(X = 4) respectively.
i.e. `"^4C_0 (4/5)^0 (1/5)^(4 - 0)`, `"^4C_1 (4/5)^1 (1/5)^(4 - 1)` , `"^4C_2 (4/5)^2 (1/5)^(4 - 2)`, `"^4C_3 (4/5)^3 (1/5)^(4 - 3)` and `"^4C_4 (4/5)^4 (1/5)^(4 - 4)`
i.e. `1 (1)(1/5)^4, 4(4/5)*(1/5)^3, (4 xx 3)/(1 xx 2) (16/25)(1/25), 4(64/125)(1/5) and 1 xx (4/5)^4 (1/5)^0`
i.e. `(1/5)^4, 16/5 (1/5)^3, 96/5^2 (1/5^2), 256/5^3 (1/5) and 256/5^4`
i.e. `1/5^4, 16/5^4, 96/5^4, 256/5^4, 256/5^4`
OR `1/625, 16/625, 96/625, 256/625 and 256/625`
APPEARS IN
RELATED QUESTIONS
A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at most 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
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:
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 = ______.
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 ≥ 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 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 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?
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 7 or 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 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.
Fill in the blank :
In Binomial distribution probability of success Remains constant / independent from trial to trial.
If X ~ B(n, p) with n = 10, p = 0.4, then find E(X2).
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 ______.
If X∼B (n, p) with n = 10, p = 0.4 then E(X2) = ______.
