A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than 9, given that the black resulted in a 5 is

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:

Let A and B be independent events such that P (A) = 0.3 and P (B) = 0.4, then

Match List-I with List-II

Choose the correct answer from the options given below:

The probability that exactly one of them complete the task on time is

The variance of number of heads in three tosses of a coin is :

Five bad apples are mixed with 15 good apples accidently. Let the random variable X be the number of bad apples in a draw of two apples, then mean of X is

The probability that in a year of the 22nd century choosen at random, there will be 53 Sundays is: