$A$ bag contains $3$ black and $4$ white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white,is

If two dice are rolled,then the probability of getting a multiple of $3$ as the sum of the numbers appeared on the top faces of the dice,given that their sum is an odd number,is

Let $A$ and $B$ be not mutually exclusive events. If $P(A) = \frac{4}{9}$ and $P(A \cap \bar{B}) = \frac{3}{7}$,then find $P\left(\frac{B}{A}\right)$.

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

If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$,then which of the following is correct?

$A$ black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than $9,$ given that the black die resulted in a $5$.