$A$ number is chosen at random from the first ten natural numbers. The probability that the number is odd and a perfect square is

The probability that a non-leap year contains $53$ Sundays is

$A$ number $n$ is chosen at random from $\{1, 2, 3, 4, \ldots, 1000\}$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ is:

Three coins are tossed once. Let $A$ denote the event 'three heads show',$B$ denote the event 'two heads and one tail show',$C$ denote the event 'three tails show',and $D$ denote the event 'a head shows on the first coin'. Which events are mutually exclusive?

Three coins are tossed simultaneously. Consider the events $E$: 'three heads or three tails',$F$: 'at least two heads',and $G$: 'at most two heads'. Of the pairs $(E, F)$,$(E, G)$,and $(F, G)$,which are independent and which are dependent?

If $A$,$B$,and $C$ are mutually exclusive and exhaustive events of a sample space $S$ such that $P(B) = \frac{3}{2} P(A)$ and $P(C) = \frac{1}{2} P(B)$,then $P(A) = $