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

$A$ bag contains $3$ red and $3$ white balls. If two balls are drawn one after another,what is the probability that they are of different colors?

If two balanced dice are tossed once,the probability of the event that the sum of the integers appearing on the upper faces of the two dice is $9$ is:

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
$A:$ the sum is greater than $8$.
$B:$ $2$ occurs on either die.
$C:$ the sum is at least $7$ and a multiple of $3$.
Which pairs of these events are mutually exclusive?

If two dice are thrown together,then the probability that the sum of the numbers appearing on them is a prime number is:

If $A, B$ and $C$ are mutually exclusive and exhaustive events of a random experiment such that $P(A) = \frac{2}{3} P(B)$ and $P(B) = 2 P(C)$,then $P(A \cup C) =$