# what are the odds of 3+ people winning the lottery?

I was on the 10 o’clock evening news last night on NBC15 Madison to talk about the odds of three people in Dane County winning the Supercash! lottery. There are about half a million residents, and I have no idea how many people play the lottery every day, but I was able to do a few quick back of the envelope calculations

• If everyone in Dane County plays the lottery every day (unrealistic!) then we would expect 3+ people to win in a single day to happen every 0.71 years.
• If half of everyone in Dane County plays the lottery every day (almost all the adults, still unrealistic!) then we would expect 3+ people to win in a single day to happen every 5.12 years.
• If 1 in 10 people in Dane County play the lottery every day (in the ballpark of reality) then we would expect 3+ people to win in a single day to happen every 584 years.
• If 1 in 20 people in Dane County play the lottery every day (in the ballpark of reality) then we would expect 3+ people to win in a single day to happen every 4620 years.

I am having trouble embedding the video, but you can go here to see it.

Area nerd explains the probability of winning the lottery, compares the likelihood of winning the lottery to being eaten by a bear.

Tips for working with the media:

• You can overthink it. “Make things as simple as possible, but not simpler.” Except in this case, even simpler is good. You don’t have a couple of minutes to break apart a concept. Insightful comments that can fit in a tweet are good.
• News moves fast. I was recorded 2 hours after getting the call for the story. In that two hours, I had to take care of things at work, pick up my daughters, and go home. There was very little time for research.
• Crunch some numbers ahead of time to put things into perspective. You may only have time for back of the envelope calculations. If you don’t have all the information (like how many people play the lottery every day), make an assumption and test a few values.
• I find it helpful to explain probabilities in terms of odds (1 in 1.6 million) and expected time to observe the event (every 584 years).
• If you’re dealing with rare events, be prepared to compare the rare event to other rare events. Someone will definitely ask about the odds of getting struck by lightning.

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#### 3 responses to “what are the odds of 3+ people winning the lottery?”

• Luis Duran

Hello Dr. Mclay, congratulations nice interview. How were you able to come up with the 0.71 , 5.12 and 584 years? can you share a little bit of the way you calculated this?

Thanks,

• Laura McLay

Good question! I estimated probabilities using a Binomial(N,1/1.6M) distribution, where X~number of winners, assuming that the numbers on each ticket is randomly generated, and N is the number of tickets sold, and success probability equal to the probability of having a successful ticket. The lack of independence was mentioned in the story: sometimes a husband and wife accidentally buy tickets with the same numbers separately from one another and they could both win.

• Turgid Jacobian

Hah, excellent!