Two fair dice are rolled. The probability of the sum of digits on their faces being greater than or equal to $10$ is

The probability that at least one of the events $A$ and $B$ occurs is $3/5$. If $A$ and $B$ occur simultaneously with probability $1/5$,then $P(A') + P(B')$ is (in $/5$)

The probability that a non-leap year selected at random will have $53$ Sundays or $53$ Saturdays is

$A$ coin is tossed three times. Consider the following events:
$A$: 'No head appears',
$B$: 'Exactly one head appears',
$C$: 'At least two heads appear'.
Do they form a set of mutually exclusive and exhaustive events?

An experiment consists of tossing a coin and then throwing it a second time if a head occurs. If a tail occurs on the first toss,then a die is rolled once. Find the sample space.

$X$ speaks truth in $60\%$ and $Y$ in $50\%$ of the cases. The probability that they contradict each other in narrating the same incident is