Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be :

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:

The probability of not getting $53$ Tuesdays in a leap year is :

Under which of the following conditions the Poisson distribution is the limiting case of, binomial distribution:

(A) The number of trials is indefinitely large.

(B) The probability of success for each trial is indefinitely small.

(C) The product of the number of trials and the probability of success for each trial is finite.

(D) The probability of success for each trial is indefinitely large.

Choose the correct answer from the options given below:

4 cards are drawn from a standard deck of 52 cards. The probability of drawing exactly 2 cards of the same suit is:

A random variable X follow Poisson distribution such that P(X=1) = 2P(X=2) , then P(X=0) is

Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probability, that both coins are unbiased is: