Nitin has taken the subjects mathematics, physics and chemistry. The probability of him getting grade A in these subjects are respectively 0.2, 0.3 and 0.9. Getting grades in different subjects are regarded as independent events. The probability of getting A grade by him, either in mathematics or physics, is

In the family mother, father and son stand up at random for a family picture. Define following two events :

$E$ = [Son stands at one of the two ends in the picture]

$F$ = [Father stands in the middle of the picture]

The value of $P(F/E)$ is :

Let A and B be two events. Then which of the following statements are TRUE?

(A) $P(B|A) = \frac{P(A \cap B)}{P(A)}$, provided $P(A) \neq 0$

(B) $P(B') = 1 + P(B)$

(C) $P(A \cup B) = P(A) + P(B) + P(A \cap B)$

(D) $P(A \cap B) = P(A).P(B)$ If A and B are independent events

Choose the correct answer from the options given below:

A man is known to speak truth 8 out of 11 times. He takes out two balls from a bag containing 3 white, 2 black and 5 red balls. What is the probability that he reports both the balls to be white?

If A and B are two events such that $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$, then which of the following statements are true?

(A) A and B are independent events

(B) $P(A | B) = \frac{3}{4}$

(C) $P(A' | B') = \frac{5}{8}$

(D) $P(A' | B) = \frac{1}{4}$

Choose the correct answer from the options given below:

Let A, B, C be three events. If the probability of occurring exactly one out of A and B is $\frac{3}{5}$, exactly one of B and C is $\frac{1}{5}$, exactly one of C and A is $\frac{3}{5}$ and that of occurring of three events is $\frac{4}{25}$, then the probability of occurring at least one of them is

Let X be random variable which assumes $x_1$, $x_2$, $x_3$, $x_4$ such that 2P(X=$x_1$)= 3P(X=$x_2$)=P(X=$x_3$)=5P(X=$x_4$) , then the probability distribution of X is