Probability

Two dices are rolled. If both dices have six faces numbered 1,2,3,5,7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is:

In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is

The mean and variance of a binomial distribution are and $\frac{\alpha }{3}$ respectively. If P(X = 1) = $\frac{4}{243}$ then P(X = 4 or 5) is equal to:

Let X be a binomially distributed random variable with mean 4 and variance $\frac{4}{3}.$ Then, $54P\left(X\le 2\right)$ is equal to

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If ${\sigma }^2$ is the variance of X, then $100{\sigma }^2$ is equal to………

Let A and B be two events such that $P\left(A|B\right)=\frac{2}{5},P\left(A|B\right)=\frac{1}{7}andP\left(A\cap B\right)=\frac{1}{9}.$ Consider $\left(S1\right)P\left(A\text{'}\cup B\right)=\frac{5}{6},$

$\left(S2\right)P\left(A\text{'}\cap B\text{'}\right)=\frac{1}{18}$

Then

The number of positive integers k such that the constant term in the binomial expansion of ${\left(2x^3+\frac{3}{x^k}\right)}^{12},x\ne 0is{2}^8.\mathcal{l},where\mathcal{l}$  is an odd integer, is……….

The probability, that in a randomly selected 3-digit number at least two digits are odd, is

Let $S=\left\{E_1,E_2,......,E_8\right\}$  be a sample space of a random experiment such that P(E_n) = $\frac{n}{36}$  for every n = 1, 2,……, 8. then the number of elements in the set $\left\{A\subseteq S:P\left(A\right)\ge \frac{4}{5}\right\}$ is……….