$A$ single letter is selected at random from the word $PROBABILITY$. The probability that the selected letter is a vowel is

$A$ coin is tossed twice. The probability of getting head both the times is

If $x$ is chosen at random from the set $\{1, 2, 3, 4\}$ and $y$ is chosen at random from the set $\{5, 6, 7\}$,then the probability that $xy$ will be even is

The probability that two randomly selected subsets of the set $\{1, 2, 3, 4, 5\}$ have exactly two elements in their intersection is:

If $A$ and $B$ are events such that $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(\overline{A}) = \frac{2}{3}$,then what is the value of $P(\overline{A} \cap B)$?

For independent events $A_1, A_2, \dots, A_n$,$P(A_i) = \frac{1}{i + 1}$ for $i = 1, 2, \dots, n$. Then the probability that none of the events will occur is: