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 :

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate solve any problem is $${4 \over 5}$$ , then the probability that he is unable to solve less than two problems is :

Let a random variable X have a binomial distribution with mean 8 and variance 4. If $$P\left( {X \le 2} \right) = {k \over {{2^{16}}}}$$, then k is equal to :

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :