Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that one of them is black and the other is red.

$A$ box contains $b$ blue balls and $r$ red balls. $A$ ball is drawn randomly from the box and is returned to the box with another ball of the same colour. The probability that the second ball drawn from the box is blue,is

Two persons $A$ and $B$ take part in a shooting competition. $A$ can hit the target with a probability of $0.6$. $B$ can hit the target with a probability of $0.8$. $A$ takes the first shot,after which they shoot alternately. The probability that $A$ wins the competition is

$A$ computer program has two modules $X$ and $Y$ and errors in them occur independently. $X$ has an error with probability $0.1$ and $Y$ has an error with probability $0.3$. If an error in $X$ alone causes the program to crash with probability $0.5$, an error in $Y$ alone causes the program to crash with probability $0.7$, and an error in both $X$ and $Y$ causes the program to crash with probability $0.8$, then the probability that the program crashes is

$A$ speaks truth in $75 \%$ of the cases and $B$ in $80 \%$ of the cases. Then,the probability that their statements about an incident do not match,is

If $5$ distinct balls are placed at random into $5$ cells, then the probability that exactly one cell remains empty is (in $/ 125$)