$A$ die is rolled. Let $E$ be the event "die shows $4$" and $F$ be the event "die shows an even number". Are $E$ and $F$ mutually exclusive?

$A$ bag contains $5$ black balls, $4$ white balls and $3$ red balls. If a ball is selected at random, the probability that it is a black or a red ball, is

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice and $E_k = \{(a, b) \in S : ab = k\}$. If $p_k = P(E_k)$, then which of the following is correct?

The probability of getting at least one tail in $4$ throws of a coin is

Check whether the following probabilities $P(A) = 0.5$,$P(B) = 0.4$,and $P(A \cup B) = 0.8$ are consistently defined.

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?