SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 3 - Binomial Distribution [Latest edition]

In a Binomial distribution with n = 4, if 2P(X = 3) = 3P(X = 2), then value of p is ______

Given that X ~ B(n, p). If n = 10, p = 0.4, then E(X) = ______

For X ~ B(n, p), if V(X) = 2.4 and p = 0.4, then n = ______

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 = ______

If X ~ B(n, p), E(X) = 12, V(X) = 4, then find n

For Bernoulli Distribution, state formula for E(X) and V(X).

For X ~ B(n, p) and P(X = x) = `""^8"C"_x(1/2)^x (1/2)^(8 - x)`, then state value of n and p

State the formula for p.m.f. of Binomial Distribution

A die is thrown. If X denotes the number of positive divisors of the outcomes, then find the range of random variable X

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.

Given X ~ B(n, p). If E(X) = 6, V(X) = 4.2, find n and p

If X ~ B(n, p) with n = 10, p = 0.4, then find E(X²).

If X ~ B(6, p) and 2P(X = 3) = P(X = 2), then find p

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)

A Fair coin is tossed 5 times, find the probability that coin shows exactly three times head

A fair coin is tossed 5 times, find the probability that no head 

The probability that certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive

Find the probability of guessing correctly at least nine out of ten answers in a "true" or "false" objective test

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

A fair coin is tossed 8 times. Find the probability that it shows heads at least once

The probability that a person who undergoes a kidney operation will be recovered is 0.5. Find the probability that out of 6 patients who undergo similar operation none will recover

The probability that a person who undergoes a kidney operation will be recovered is 0.5. Find the probability that out of 6 patients who undergo similar operation half of them recover.