Ten cards are numbered from 1 to 10. A and B are playing a game by drawing a card, alternately, with replacement, till one gets a prime number then the probability of B's winning if A started the game is

60% members of a committee favour a certain proposal and 40% members oppose the proposal. A member is selected and let the random variable X = 0 if he opposes and X = 1 if he is in favour. Then the variance of the random variable X is

If A and B are two independent events, then which of the following is/are true?

(A) $P(A \cap B) = 0$

(B) $P(A \cup B) = 1 - P(A')P(B')$

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

(D) $P(A \cap B) = P(A)P(B)$

Choose the correct answer from the options given below:

The monthly expectation of a two-wheeler accident at a particular railway crossing is 0.02. What is the probability that in a specific month, no accident occurred? (given $e^{-0.02} = 0.9802$)

If E and F are two events such that P(E) = 0.8, P(F) = 0.7 and P(E ∩ F) = 0.6 then $P(\bar{E}/\bar{F})$ is:

The mean of the number of heads in a simultaneous toss of three coins is :

If the binomial distribution $X\sim B(n, p)$ of mean 3 and variance $\frac{3}{2}$, $(p + q) = 1$, then which of the following is/are TRUE?

(A) $q = \frac{1}{2}$, $n = 6$

(B) $P(X \leq 5) = \frac{63}{64}$, $p = \frac{1}{2}$

(C) $q = \frac{1}{3}$, $p = \frac{2}{3}$

(D) $P(X = 4) = \frac{15}{64}$, $n = 6$

Choose the correct answer from the options given below: