Let A and B be two independent events such that
P(A) = $${1 \over 3}$$ and P(B) = $${1 \over 6}$$.
Then, which of the following is TRUE?

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $${{1 \over 4}}$$ . If the probability that at most two machines will be out of service on the same day is $${\left( {{3 \over 4}} \right)^3}k$$, then k is equal to :

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value of k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value -1. Then the expected value of X, is :

A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :