List of top Mathematics Questions on binomial distribution asked in MHT CET

The probability of a shooter hitting a target is \( \frac{3}{4} \). Find the probability of hitting the target exactly 4 times in 5 shots.
In a Binomial distribution with \(n=10\) and \(p=0.4\), find the variance.
If (X \sim B(35, p)) such that (7P(X = 0) = P(X = 1)) then the value of (\frac{P(X=15){P(X=20)}) is equal to
Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then ( E(X^2) = )
If $f(1) = 1, f'(1) = 3$, then the derivative of $f(f(f(x))) + (f(x))^2$ at $x = 1$ is
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
The modulus of the square root of the conjugate of $-7 + 24\sqrt{-1}$ is __________
The probability that a certain kind of component will survive a given test is \(\frac{2}{3}\). The probability that at most \(2\) components out of \(4\) tested, will survive is
If (X \sim B(35, p)) such that (7P(X = 0) = P(X = 1)) then the value of (\frac{P(X=15){P(X=20)}) is equal to
Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then ( E(X^2) = )

If \( X \sim B(35, p) \) such that \( 7P(X = 0) = P(X = 1) \), then the value of

\[ \frac{P(X = 15)}{P(X = 20)} \] 

is ______.

Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then ( E(X^2) = )
In a Binomial distribution with $n=4$ if $2P(X=3)=3P(X=2)$, then the variance is
It is observed that 25% of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the probability that at least 5 of them will be solved is
For $X \sim B(n, p)$, if $p = 0.6$ and $E(X) = 6$, then $\text{Var}(X) =$
If the sum of mean and variance of a binomial distribution for 5 trials is 1.8, then probability of a success is
The p.m.f. of a random variable $X$ is $P(X = x) = \frac{1}{2^5} \binom{5}{x}, x = 0, 1, 2, 3, 4, 5$, then
If $X \sim B(4, p)$ and $P(X = 0) = \frac{16}{81}$, then $P(X = 4) =$
A lot of 100 bulbs contains 10 defective bulbs. Five bulbs selected at random from the lot and sent to retain store, then the probability that the store will receive at most one defective bulb is
Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution of number of queens is
For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is \( \frac{4}{5} \), then the probability that he is unable to solve less than two problems is