Remember that the probability that a birth results in a boy is about .51. You offer a bet to an unsuspecting friend. Each day you will call the local hospital and find out how many boys and how many girls were born the previous day. For each girl, you will give your friend $ 1 and for each boy your friend will give you $ 1.
a. Suppose that on a given day there are three births. What is the probability that you lose $ 3 on that day? What is the probability that your friend loses $ 3?
b. Notice that your net profit is $ 1 if a boy is born and –$ 1 if a girl is born. What is the expected value of your profit for each birth?
c. Using your answer in part (b), how much can you expect to make after 1000 births?