expected value of your ticket

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?)