If $X$ is a normal variate with mean 12 and standard deviation 4, then $P[X \ge 20]$ is:

[Given that: $P[0 \le Z \le 2] = 0.4772]$

Given that the events A and B are mutually exclusive such that $P(A)=\dfrac{1}{2}$, $P(A\cup B)=\dfrac{2}{3}$ and $P(B)=p$, then the value of $p$ is:

A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is

Let X denote the number of hours a person watches television during a randomly selected day. The probability that X can take the value $x_i$, has the following form, where $k$ is some unknown constant.

$P(X=x_i) = \begin{cases} 0.5 & \text{if } x_i=0 \\ kx_i & \text{if } x_i=1 \\ k(4-x_i) & \text{if } x_i=2 \text{ or } 3 \\ 0 & \text{otherwise} \end{cases}$

The probability that the person watches at most 2 hours of television on a selected day is :

Match List-I with List-II

Choose the correct answer from the options given below:

The probability that it will rain on any particular day is 50%. The probability that it rains only on the first 4 days of the week is:

In a game, a person is paid Rs. 2 if he gets all heads or all tails when three coins are tossed, and he will pay Rs. 2 if either one or two heads show. What can he expect to win on an average per game?