$A$ fair die is tossed until a six is obtained. Let $X$ be the number of required tosses,then the conditional probability $P(X \geq 5 \mid X > 2)$ is:

If $A$ and $B$ are two events such that $P(A \cap B) = 0.1$,and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12x^2 - 7x + 1 = 0$,then the value of $\frac{P(\overline{A} \cup \overline{B})}{P(\overline{A} \cap \overline{B})}$ is:

If $80 \%$ of flights depart on time, $70 \%$ of flights arrive on time and $65 \%$ of flights depart on time and arrive on time, then the probability that a flight that has just departed on time will arrive on time is

$A$ die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of $4$. Then the conditional probability that the score $4$ has appeared at least once is

If $P(A)=0.8, P(B)=0.5$ and $P(B | A)=0.4,$ find $P(A | B).$

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?