Let’s say that your company is having a holiday party. As part of the festivities, they give gifts of lottery tickets. In Florida, we have a game called Lotto. The Florida Lotto has a person pick 6 numbers (numbers can be 1 to 53). A person wins a prize if he or she matches 3, 4, 5, or 6 of the numbers. If the person matches all 6, he or she wins the major prize, which is determined by how many people purchase tickets (usually at least 3 million dollars). If a person matches 5 numbers, he or she wins a smaller prize (around $3000). If a person matches 4 numbers, he or she wins $70. The lowest prize is for matching 3 out of the 6 numbers and that prize is $4.50.

The Lotto odds of winning are listed on the Florida Lotto website. However, your company is buying multiple tickets, so what are the odds of at least one person winning a prize (all tickets are purchased with random numbers)?

To take one example, the probability of matching 3 out of the 6 numbers is about .014. Thus, you only have a 1.4% chance that your one ticket matches 3 out of 6 numbers. If there are 72 employees, then the probability that not one of those tickets matches 3 out of 6 numbers is .359 (.014 multiplied by itself 72 times). Thus, there is a 64% chance that someone will win $4.50.

Here are the chances for at least one person winning the prizes if your company buys 72 tickets:
3 out of 6 numbers: 64.1%
4 out of 6 numbers: 4.96%
5 out of 6 numbers: .088%
6 out of 6 numbers: .00031%
Someone winning at least one prize: 65.93%