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

The probability distribution of X is as follows:

Find k and P[X < 2]

Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as number greater than 4 appears on at least one die.

Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as six appears on at least one die

Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings drawn.

If the p.m.f of a r. v. X is

P(x) = `c/x^3`, for x = 1, 2, 3

        = 0, otherwise

then E(X) = ______.

Find the mean of number randomly selected from 1 to 15.

For the following probability density function of a random variable X, find P(X < 1).

`{:(f(x) = (x + 2)/18,";"  "for" -2 < x < 4),(               = 0,","  "otherwise"):}`

For the following probability density function of a random variable X, find P(|X| < 1).

`{:(f(x) = (x + 2)/18,";"  "for" -2 < x < 4),(               = 0,","  "otherwise"):}`

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.