Let a die be loaded in such a way that even faces are twice likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?

Let the sample space consist of non-negative integers up to 50, X denote the numbers which are multiplies of 3 and Y denote the odd numbers. Which of the following is/are correct?

1. P(X) = $${8 \over {25}}$$

2. P(Y) = $${1 \over {2}}$$

Select the correct answer using the code given below.

For two events A and B, let $$P(A) = {1 \over 2}$$, $$P(A \cup B) = {2 \over 3}$$ and $$P(A \cap B) = {1 \over 6}$$. What is $$P(\overline A \cap B)$$ equal to ?

Let A and B be two events with $$P(A) = {1 \over 3}$$, $$P(B) = {1 \over 6}$$ and $$P(A \cap B) = {1 \over {12}}$$. What is $$P(B\,|\,\overline A )$$ equal to ?