Question

1) Choose a lottery that has published odds. Make sure to post the odds in both "1 in X" format and in "p = 0.XXX" decimal format. For example, Flip a Coin has a 1 in 2 chance of being heads, p(heads) = 0.50

2) Explain why P(A and B) = 0, where P(A) = lottery number #1 is a winning jackpot ticket and P(B) = lottery number #2 is a winning jackpot ticket.  

3) If there was a really large jackpot, how many tickets might you be tempted to buy? How would it change your odds to buy multiple tickets, hoping that one of them is the jackpot winner? Would the cost of that number of tickets be worth it to you?

4) Given these odds, why do you think the lottery is so popular?

Odds of winning a jackpot for selected lottery games:

1 in 6,096,454 for Multi-Match (lottery game that costs $2 per ticket)

1 in 292,201,338 for Powerball (lottery game that costs $2 per ticket)

1 in 302,575,350 for Mega Millions (lottery game that costs $2 per ticket)

1 in 404,000,000 for Safeway Monopoly game to win $1 million

Answer 1

1)

Say a lottery has published odds of winning to be 1 in 10000, Hence p = 0.0001

2)

Winning lottery has to be one specific ticket hence chance of ticket #1 and #2 simultaneously being winning tickets is zero

3)

One would calculate the expected return he would get by entering the lottery. Then he would decide if buying is worth it or not.

4)

These lotteries are so popular because the cost of the ticket is very less compared to the expected return of jackpot. Hence people are willing to buy the lottery tickets.