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

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N - 2, \sqrt{3N}, N + 2$ are in geometric progression be $\frac{k}{48}$. Then the value of $k$ is

If $A$ and $B$ are any two events,then $P(\bar{A} \cap B) = $

When three fair dice are tossed simultaneously,find the probability that the integers on all three dice are the same.

$A, B, C$ are aiming to shoot a balloon. $A$ will succeed $4$ times out of $6$ attempts. The chance of $B$ to shoot the balloon is $3$ out of $5$ and that of $C$ is $2$ out of $3$. If the three aim to shoot the balloon simultaneously, then the probability that at least two of them hit the balloon is

Six faces of an unbiased die are numbered with $2, 3, 5, 7, 11$ and $13$. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is