$A$ game consists of tossing a coin $3$ times and noting its outcome. $A$ boy wins the game if all tosses give the same outcome (i.e.,three heads or three tails) and loses the game otherwise. The probability that the boy loses the game is

The chance of getting a doublet with $2$ dice is

Statement-$I$: If a leap year is selected at random,the probability of it having $53$ Sundays is $2/7$.
Statement-$II$: $A$ leap year has $366$ days.

Three coins are tossed. Describe two events which are mutually exclusive.

Three students $X, Y$ and $Z$ appear for an examination. The probability of $X$ passing the examination is $\frac{1}{5}$,the probability of $Y$ passing the examination is $\frac{1}{4}$ and the probability of $Z$ failing the examination is $\frac{2}{3}$. The probability that at least two of them pass the exam is

The probability that $A$ speaks truth is $4/5$,while the probability that $B$ speaks truth is $3/4$. The probability that $A$ and $B$ contradict each other when asked to reveal the fact is