Embibe Experts Solutions for Chapter: Probability, Exercise 2: Exercise 2

A six digit number is formed with the digits $0, 1, 2, 3, 4, 7$ without repetition. Then the probability that it is divisible by $4$ is

Out of $20$ consecutive numbers, three are chosen at random. The probability that their sum is even is 

If the probability density function of a random variable is given by $f\left(x\right)=\left\{\begin{array}{l}k\left(1-x^2\right), 0<x<1\\ 0, \text{elsewhere}\end{array}\right.$, then the value of $k$ is

A bag contains $10$ white and $3$ black balls. Balls are drawn without replacement till all the black balls are drawn. What is the probability that this procedure will come to an end on the seventh draw ?

If $m$ is the parameter of the Poisson distribution then the variance of the distribution is

$A$ is a set containing $n$ elements. A subset $P_1$ of $A$ is chosen at random. The set $A$ is reconstructed by replacing the elements of $P_1$. A subset $P_2$ is again chosen at random. The probability that $P_1\cup P_2$ contains exactly one element, is

A continuous random variable X has probability distribution function $f\left(x\right)=3x^2, 0\le x\le 1$, then the value of $a$ and $b$ such that $P\left(X\le a\right)=P\left(X>a\right)$

While shuffling a pack of $52$ playing cards, $2$ are accidentally dropped. The probability that the missing cards to be of different colour is