If $A$ and $B$ are any two events, then $P(A \cup B) = $

The probability that a man will be alive in $20$ years is $\frac{3}{5}$ and the probability that his wife will be alive in $20$ years is $\frac{2}{3}$. Then the probability that at least one will be alive in $20$ years, is

In a class of $125$ students $70$ passed in Mathematics, $55$ in Statistics and $30$ in both. The probability that a student selected at random from the class has passed in only one subject is

Let $S=\{1,2,3, \ldots, 2022\}$. Then the probability, that a randomly chosen number $n$ from the set $S$ such that $\operatorname{HCF}( n , 2022)=1$, is.

Two persons $A$ and $B$ throw a (fair)die (six-faced cube with faces numbered from $1$ to $6$ ) alternately, starting with $A$. The first person to get an outcome different from the previous one by the opponent wins. The probability that $B$ wins is