Commercial Prize

What is the expected number of prize tickets you will get if you buy 3 tickets?

There are 100 prizes tickets among 1000 tickets in a lottery. What isthe expected number of prize tickets you will get if you buy 3 tickets? What is a simple upper bound for the probability that you will win at least 1 prize? Compare with the actual probability. Why is the bound so close? Please help me. Thank you!

Public Comments

1. q1 3/100 = 0.3 q2 P[ win a prize on one ticket ] = 100/1000 = 0.1 P[ don't win a prize on a ticket ] = 0.9 simple upper bound = 1 - 0.9^3 = 0.271 actual probability 1 - [900/1000][899/999][898/998] = 0.27124 the bound is so close because the # of tickets is so large