If one ticket is selected at random from $30$ tickets,each with a distinct number from $1$ to $30$,then the probability that the number on the selected ticket is a multiple of $3$ or $5$ is

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in the number of girls in the family?

Three coins are tossed once. Let $A$ denote the event 'three heads show',$B$ denote the event 'two heads and one tail show',$C$ denote the event 'three tails show',and $D$ denote the event 'a head shows on the first coin'. Which events are mutually exclusive?

$A$ problem in mathematics is given to $4$ students whose chances of solving it individually are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4},$ and $\frac{1}{5}.$ The probability that the problem will be solved by at least one student is

Two cards are drawn from a pack of $52$ cards. What is the probability that both cards are red or both cards are kings?

$A$ die is loaded such that the probability of throwing the number $i$ is proportional to its reciprocal. Then the probability that $3$ appears in a single throw is