Question

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 Odds 1:292,201,338 1:11,688,054 1:913,129 1:36,525 1:14,494 1:580 1:701 1:92 1:38 Scenario Match 5+PB Match 5 Match 4PB Match 4 Match 3+PB Match 3 Match 2+PB Match 1+PB Match 0+PB Payout 85,400,000 1,000,000 50,000 100 100 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 0+PB are not 1:25 22) Find the expected value of a Powerball ticket.

Answer 1

Probability of matching all the 5 numbers and power ball is given by 20. 수)-(26)=(69-68 6766-65) (26) 292201338 Matching 0 + PB means that no number is matching but power ball number is matching. Since probability of "no number match" is not 1, hence match 0 + PB is not 1:25, this can be shown by calculations, 21. 64C5 673 69C 992 Probability of Match 05- Probability of Match 0 PB(approximately) Expected value of a power ball ticket 673 1 1 992 26 38 22. 26 nxP(n)+2+3 + 26) 13.5 26