Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to throw a sum of $9$ with both dice will win the game. If $A$ throws first,then the probability that $B$ wins the game is:

Two friends $A$ and $B$ meet every weekend either at a party or at a Sports Club. The probability that they meet at the Sports Club is $\frac{4}{9}$. The probability that they dine together at a party and at the Club are respectively $\frac{1}{3}$ and $\frac{2}{5}$. On a certain weekend, the probability that they disperse without dining together is:

If the integers $m$ and $n$ are chosen at random between $1$ and $100$,then the probability that a number of the form $7^m + 7^n$ is divisible by $5$ equals

If $A$ and $B$ are two events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{2}{3},$ then

Three urns respectively contain $2$ white and $3$ black,$3$ white and $2$ black,and $1$ white and $4$ black balls. If one ball is drawn from each urn,then the probability that the selection contains $1$ black and $2$ white balls is

Two squares are chosen at random on a chess-board. The probability that they have a side in common is