Communication, Networking, Signal and Image Processing (CS)

Question 1: Probability and Random Processes

January 2004

**2. (10 pts.)**

Identical twins come from the same egg and and hence are of the same sex. Fraternal twins have a probability $ 1/2 $ of being of the same sex. Among twins, the probability of a fraternal set is p and of an identical set is $ q=1-p $ . Given that a set of twins selected at random are of the same sex, what is the probability they are fraternal? (Simplify your answer as much as possible.) Sketch a plot of the conditional probability that the twins are fraternal given that they are of the same sex as a function of $ q $ (the probability that a set of twins are identical.)

**Note**

This problem is identical to the problem in the MBR 2004 Spring Final.