Two dice are rolled one after the other. The probability that the number on the first die is smaller than the number on the second die 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 $P(\overline{A} \cap B)$?

$A$ letter is chosen at random from the word $ASSASSINATION$. Find the probability that the letter is a vowel. (in $/13$)

Two friends $A$ and $B$ apply for a job in the same company. The probability of $A$ getting selected is $\frac{2}{5}$ and that of $B$ is $\frac{4}{7}$. Then the probability that one of them is selected is:

Each of the two boxes $P$ and $Q$ contain $100$ chits numbered from $1$ to $100$. If one chit is drawn at random from each box,then the probability that the number on the chit drawn from $P$ is the square of the number on the chit drawn from $Q$,is (in $\%$)

One card is drawn from a well-shuffled deck of $52$ cards. If each outcome is equally likely,calculate the probability that the card will not be a diamond.