For any events A and B of a sample space S, which of the following statements are TRUE? (A) $P(S | B) = 1$ (B) $P(A \cap B) = P(A) + P(B) + P(A \cup B)$ (C) $P(\bar{A} | B) = 1 - P(A | B)$ (D) $P(A | B) = \frac{P(A \cap B)}{P(B)}, P(B) \neq 0$ Choose the correct answer from the options given below:

A pair of dice is thrown until the sum of numbers appeared is a perfect square or a non-perfect square sum appeared five times in succession. If random variable $X$ denotes the number of non perfect square sums appeared, then $P(X > 0)$ is

In a game, a person is paid Rs. 2 if he gets all heads or all tails when three coins are tossed, and he will pay Rs. 2 if either one or two heads show. What can he expect to win on an average per game?

A coin is tossed 7 times. The probability of getting at least 4 heads is:

If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.001. The probability that out of 2000 individuals, more than two individuals suffer from bad reaction is:

[Given that $e^{-2} \approx 0.13534$]

Let E and F are two independent events such that $P(E)=0.35$ and $P(E\cup F)=0.60$ then which of following statements are TRUE?

(A) $P(F)=\frac{5}{13}$

(B) $P(E|\overline{F})=0.35$

(C) $P(E|\overline{F})=0.65$

(D) $P(\overline{E}|\overline{F})=0.65$

Choose the correct answer from the options given below:

A fair coin is tossed 100 times. The probability of getting head an odd number of times is