If a die is thrown at random,then the expectation of the number on it is

In a game,a man wins $₹ 40$ if he gets $5$ or $6$ on a throw of a fair die and loses $₹ 20$ for getting any other number on the die. If he decides to throw the die either until he gets a $5$ or $6$ or to a maximum of $3$ throws,then his expected gain/loss (in rupees) is:

India plays two matches each with West Indies and Australia. In any match,the probabilities of India getting $0, 1,$ and $2$ points are $0.45, 0.05,$ and $0.50$ respectively. Assuming that the outcomes are independent,the probability of India getting at least $7$ points is:

$A$ fair six-faced die is rolled $12$ times. The probability that each face turns up exactly twice is equal to:

The p.d.f. of a continuous random variable $X$ is given by $f(x) = \frac{x}{8}$ for $0 < x < 4$ and $f(x) = 0$ otherwise. Then $P(X \leq 2)$ is:

If a random variable $X$ follows a Poisson distribution such that $P(X=1) = 3P(X=2)$,then $P(X=3) =$