Let a random variable X take values 0, 1, 2, 3 with P(X=0)=P(X=1)=p, P(X=2)=P(X=3) and E(X²)=2E(X). Then the value of 8p−1 is :

The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is

If the probability that the random variable $X$ takes the value $x$ is given by

$P(X=x)=k(x+1) 3^{-x}, x=0,1,2,3 \ldots$, where $k$ is a constant, then $P(X \geq 3)$ is equal to