Q) Suppose you have bought a $20 raffle ticket. 100,000 tickets have been sold
numbered 00000-99999. Your ticket number is 75555. One ticket number will be drawn at random, and the following prizes will be awarded
. a grand prize of $1,000.000 for the person with the ticket that matches ticket number exactly
. several prizes of $1,000 for people whose ticket numbers match on the last 3 digits but
not on all 5 digits) [For example, you would win $1000 if the winning ticket number were 00555 or 25555.]
(a) What is the expected value of your ticket?
(b) Suppose your friend has learned the winnmg ticket number and teases you
by telling you that it contains exactly 4 fives. Although this doesn’t guarantee that you
have won a prize, it clearly improves your chances. Given this additional information
what is the new expected value of your ticket?
(Hint: How many different 5-digit ticket numbers have exactly 4 fives?)