HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

Find k, if the following function is p.d.f. of r.v.X:

f(x) = `{:(kx^2(1 - x)",", "for"  0 < x < 1),(0",", "otherwise"):}`

Given that X ~ B(n= 10, p). If E(X) = 8 then the value of

p is ...........

(a) 0.6

(b) 0.7

(c) 0.8

(d) 0.4

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.

The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 4 will hit the target.

A fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times.

A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is `1/100`. What is the probability that he will win a prize at least once. 

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 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 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.

Let X ~ B(10, 0.2). Find P(X = 1).

Let X ~ B(10, 0.2). Find P(X ≥ 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.

Find the probability that the visitor obtains answer yes from at least 2 pupils:

1. when the number of pupils questioned remains at 4.
2. 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.

Given that X ~ B(n = 10, p), E(X) = 8, then value of p = ______

Bernoulli distribution is a particular case of binomial distribution if n = ______

A r.v. X ~ B(n, p). If the values of mean and variance of X are 18 and 12 respectively, then find total number of positive values of X.

Let the p.m.f. of r.v. X be P(x) = `""^4"C"_x (5/9)^x (4/9)^(4 - x)`, x = 0, 1, 2, 3, 4. Find E(X) and Var(X)