Let us assume you have two stocks with the following probabilities of return: P(0.5,0.5) = 0.4, P (0.5, 0.5) = 0.2, P (0.5, 0.5) = 0.15, P (0.5, 0.5) = 0.25.

1. What is going to be the probability of the first stock returning 0.5?

2. What is going to be the probability of the second stock returning 0.5?

3. If X is the outcome of the first stock and Y is the outcome of the second stock what is : P (X = 0.5|Y = 0.5)?