Assume that each born child is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that the youngest is a girl?

Two dice are thrown and the sum of the numbers appearing on the dice is observed to be a multiple of $4$. If $p$ is the conditional probability that number $4$ has appeared at least once, then $3p + 2 =$

$A$ coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which the first throw is a head,then $P(E|F) = $

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes,the number of outcomes that $B$ must have so that $A$ and $B$ are independent,is

If $A$ and $B$ are two events such that $P(A \cup B) = P(A \cap B)$,then the true relation is

It is given that $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$. Then $P(B) = $?