$A$ coin is tossed $3$ times. The probability of getting exactly two heads is

Three coins are tossed. Describe three events which are mutually exclusive and exhaustive.

One card is drawn from each of two ordinary packs of $52$ cards. The probability that at least one of them is an ace of hearts is:

$A$ bag contains $7$ green and $5$ black balls. $3$ balls are drawn at random one after the other. If the balls are not replaced,then the probability of all three balls being green is

$A$ coin is tossed. If it shows a tail,we draw a ball from a box which contains $2$ red and $3$ black balls. If it shows a head,we throw a die. Find the sample space for this experiment.

Thirty-two persons $X_1, X_2, \ldots, X_{32}$ are randomly seated around a circular table at equal intervals. Two persons $X_i$ and $X_j$ are said to be within earshot of each other if there are at most three persons between them on the minor arc joining $X_i$ and $X_j$. The probability that $X_1$ and $X_3$ are within earshot of each other is: