The North Carolina Education Lottery website has the following payout and odds for the Powerball. In this game, a ticket costs $2. You choose five different numbers from 1 to 69 and a so-called powerball number from 1 to 26. Scenario Match 5+ PB Match 5 Odds 1:292,201,338 1:11,688,054 Payout 85,400,000 1,000,000 Match 4 + PB 1:913,129 50,000 Match 4 1:36,525 100 Match 3+PB 1:14,494 100 Match 3 1:580 7 Match 2+PB 1:701 7 Match 1+PB 1:92 4 Match 0+PB 1:38 4 20) Show your calculations verifying the odds of matching 5+ PB.* 21) Since there are 26 balls in the Powerball drawing, explain, with or without calculation, why the odds of matching O+PB are not 1:25. 22) Find the expected value of a Powerball ticket.