$A$ card is selected from a pack of $52$ cards. How many points are there in the sample space?

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?

If $X_1, X_2, \ldots, X_n$ are $n$ independent events such that $P(X_r) = \frac{1}{r+1}$ for $r = 1, 2, \ldots, n$,then the probability that none of the $n$ events occur is

If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$,$P(\bar{A} \cup \bar{B}) = \frac{7}{10}$,and $P(B) = \frac{2}{5}$,then $P(A)$ equals

$A$ bag contains $6$ white,$5$ black,and $4$ red balls. Find the probability of getting a white or a black ball when one ball is drawn from the bag.

$A$ coin and a six-faced die,both unbiased,are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is: