If $E$ and $F$ are events such that $P(\overline{F}) = 0.7$ and $P(E \cap F) = 0.2$,then $P(E \mid F)$ is

In a class consisting of $40$ boys and $30$ girls,$30 \%$ of the boys and $40 \%$ of the girls are good at Mathematics. If a student selected at random from that class is found to be a girl,then the probability that she is not good at Mathematics is

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:

If $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$,then $P(B/A) = $

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

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is