$A$ couple has two children. One of them is a boy. What is the probability that the other child is also a boy?

Two cards are drawn from a pack of $52$ playing cards one after the other. If $p_1$ is the probability of getting a queen in the first draw and a diamond card in the second draw when the first card drawn is replaced, and $p_2$ is the probability of the same event when the first card drawn is not replaced, then $\frac{p_1}{p_2} = $

Given that the two numbers appearing on throwing two dice are different,find the probability of the event 'the sum of numbers on the dice is $4$.'

Let $X$ be a random variable which takes values $1, 2, 3, 4$ such that $P(X=r) = K r^3$ where $r = 1, 2, 3, 4$. Then:

For two events $A$ and $B$,if $P(A) + P(B) - P(A \cap B) = P(A)$,then . . . . . . .

If $2$ cards drawn at random from a well-shuffled pack of $52$ playing cards are from the same suit, then the probability of getting a face card and a card having a prime number is