If $A$ and $B$ are two events such that $P(A) = \frac{1}{3}$,$P(B) = \frac{1}{4}$ and $P(A \cap B) = \frac{1}{5}$,then $P\left( \frac{\overline{B}}{\overline{A}} \right) = $

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

Three dice are thrown. Given that the sum of the numbers on them is $8$,what is the probability that at least one of them shows a $4$?

$A$ cubical die with faces marked $1, 2, 3, ..., 6$ is tossed such that the probability of throwing the number $t$ is proportional to $t^2$. The probability that the number $5$ has appeared,given that the number turned up is not even,is:

Let $S$ be the sample space of all $3 \times 3$ matrices with entries from the set $\{0, 1\}$. Let the events $E_1$ and $E_2$ be given by $E_1 = \{A \in S : \operatorname{det} A = 0\}$ and $E_2 = \{A \in S : \text{sum of entries of } A \text{ is } 7\}$. If a matrix is chosen at random from $S$,then the conditional probability $P(E_1 \mid E_2)$ equals:

Three coins are tossed. If one of them shows tail,then the probability that all three coins show tail,is