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Is buying lottery tickets a good investment?
Most of what you hear is that playing the lottery is a waste of money. While it is fun to dream about hitting
the jackpot, you are essentially throwing away your money is what most people believe. However, there is a
claim that purchasing lottery tickets is a good investment - as long as the jackpot is large enough. Let's
investigate this idea!
In addition to the jackpot, there are smaller prizes that can also be won. Here are the possible ways to "win"
and the payouts for the Powerball lottery. The cost of one ticket is $2
The Powerball - $4 (+$2 profit)
If your Powerball matches the one that is drawn you will get your $2 ticket purchase back and a couple bucks more, for a
total of $4. The probability of your ticket matching only the Powerball is 1 in 38.
1 number plus the Powerball - still $4 (+$2 profit)
If you choose one correct number plus the Powerball you'll receive $4 again. The probability is 1 in 91.
2 numbers plus the Powerball - $7 (+$5 profit)
If your ticket matches two numbers and the Powerball you'll get $7, the probability is 1 in 701.
3 numbers - $7 again (+$5)
The probability of getting three correct numbers is 1 in 579.
3 numbers plus the Powerball - $100 (+$98)
A ticket that matches three numbers and the Powerball gets $100. The probability is 1 in 14,494.
4 numbers - $100 ($98)
The probability of buying a ticket containing four numbers without the Powerball is 1 in 36,525.
4 numbers plus the Powerball - $50,000 ($49,998)
The probability for hitting four numbers plus the Powerball is 1 in 931,129.
5 numbers - $1 million (+$999,998)
To get the $1 million prize you'll need to match the numbers on the five white balls drawn without the Powerball, which
has a probability of 1 in 11,688,053.
Powerball jackpot - ?????
If a ticket matches all 5 numbers and the Powerball, you win the Jackpot! The probability of winning is 1 in 292,201,338.
The value of the jackpot changes depending on how long it has been since somebody has won and if multiple tickets win
the jackpot in the same drawing.
About 4% of lottery tickets are winners, in other words, the probability of not winning is 24/25.
Show work on a separate sheet of paper!
1. If the jackpot winnings were $10 million, what is the expected value of a lottery ticket?
2. IF the jackpot winnings were $1.5 billion, what is the expected value of a lottery ticket?
3. What does the jackpot value have to be in order for the expected value to be $0? In other words, a break even
value.
4. What is something we are not considering in our calculations?
