Question 1. Romeo and Juliet agreed to meet at midnight (12AM). They independently arrived at a time chosen uniformly at random between 11.55PM and 12.04AM (measured in minutes).

a. What is the probability that they do meet?

b. Given that they did meet, which is more likely: that they were BOTH late (arrived 12.01 to 12.04); or that they were BOTH early? (arrived 11.55 to 11.59)?

Back up your answer with calculations, ie: P(both late | they met), and P(both early | they met)

Question 2. Let X be the number of spades in 4 cards dealt from a well-shuffled deck of 52 cards containing 13 spades.

a. Find the distribution of X. (That is, find P(X=0), P(X=1),...P(X=4)) b. Find E(X)