Question: A lottery game has the following rule: pick 5 distinct numbers from a set of 59.

a. The smallest prize winner picks exactly one number out of 5 correctly. Use hypergeometric distribution to find the probability of winning the smallest prize. (3)

b. The grand prize winner picks all 5 numbers out of 5 correctly. Use hypergeometric distribution to find the probability of winning the grand prize. (3)

c. (3 extra credit, no partial credit) Read the instruction of how to play the Power Ball at http://www.powerball.com/powerball/pb_howtoplay.asp. Find the probability of winning $4 (two ways) on a $2 play. Must show all work.

Note: if your calculator cannot take the super large number, you can always find an online calculator, as long as you search “Hypergeometric calculator”.