Three friends A, B and C are playing with a pair of dice. They throw two dice alternately. Coming of a doublet on two dice leads to a success and the game stops. If A starts the game, then the probability of his winning, is :

If E and F are two events such that $P(E \cup F)=P(E)$, then

If A and B are event such that $P(A)=\dfrac{1}{2}$, $P(B)=p$ and $P(A \cup B)=\dfrac{3}{5}$ then which of following statements is/are TRUE?

(A) Events A and B are independent if $p=\dfrac{1}{5}$

(B) Events A and B are independent if $p \in (0,1) \sim \left\{\dfrac{1}{5}\right\}$

(C) Events A and B are independent then $P(A \cap B)=\dfrac{1}{10}$

(D) Event A and B are independent then $P(A \cap B)=\dfrac{9}{10}$

Choose the correct answer from the options given below:

If A and B are two independent events with $P(A) = \frac{1}{5}$ and $P(B) = \frac{1}{3}$, then $P(A'/B)$ is:

Two thirds of the students in a class are boys and the rest are girls. It is known that the probability of a girl getting a first class is 0.25 and that of a boy getting a first class is 0.28, then the probability that a student chosen at random will get first class marks in the subject is

The mean number of heads in two tosses of a coin is :

The probability that A hits a target is $\frac{1}{5}$ and the probability that B hits it is $\frac{2}{3}$. The probability that the target will be hit if both A and B shoot at it independently is: