If $A$ and $B$ are independent events with $P(A) = \frac{1}{3}$ and $P(B) = \frac{2}{7}$,then the value of $P\left(\frac{A}{B^C}\right)$ is

If events $A$ and $B$ are such that $P(A) = \frac{1}{4}$, $P(A \cap B) = \frac{1}{10}$ and $P(A|B) = 2P(B|A)$, then $P(B) = ..........$

One ticket is selected at random from $50$ tickets numbered $00, 01, 02, \ldots, 49$. The probability that the sum of the digits on the selected ticket is $8$,given that the product of these digits is zero,equals:

$A$ and $B$ are independent events of a random experiment if and only if

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11$,given that $5$ appears on the first die?

Given that $A$ and $B$ are two events such that $P(B) = \frac{3}{5}$,$P\left(\frac{A}{B}\right) = \frac{1}{2}$,and $P(A \cup B) = \frac{4}{5}$,then $P(A)$ is equal to: