Science Questions

What's my lifetime chance of winning the lottery?

Sun, 21st Oct 2012

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Question

Trevor from Norwich asked:

When we talk about the lottery, we always refer to the 14 million to 1 chance of winning it and I just wondered, if you based it on doing the lottery on a Wednesday and a Saturday, so two 1 pound stakes for instance and you started to doing it when you were 20 years old and you lived until 80. I was wondering how that wouldíve equate in lifetimes, so actual fact, itís going to take you 100 lifetimes just the realistic chance of winning it?

 

The other second part of the question is again to do with the lottery. If you do the numbers 1 - 6 in the lottery, I think people who do that are being silly on the basis of the first 3 balls come out and on the night and itís say, number 1, number 2, number 3, the chances of 4 to 10 coming out next diminishes. Is that the case?

Answer

Matt -   Letís see if we can work this out fairly quickly.  If you start playing when you're 16 and you cease playing when you're 86, is that reasonable?  It will give us 70 years of non-stop playing.  So thatís about one hundred games per year.  So, you'll end up doing about 7,000 games across your lifetime.  What you need to do is, if itís originally 1 in 14 million, weíll divide that by the 7,000 games you're going to play because you'll have 7,000 chances to win and you end up with 2,000.  So, you need to have 2,000 lifetimes to expect to win the lottery.

Trevor -   Thatís more alarming I think and then actually saying 14 million to 1, so Iíll enjoy sharing that in work tomorrow.  The second part is also to do with the lottery.  If you do the numbers 1 - 6 in the lottery. I think people who do that are being silly on the basis of the first 3 balls come out and on the night and itís say, number 1, number 2, number 3, the chances of 4 to 10 coming out next diminishes.  Is that the case?

Matt -   If you look at the lottery as a whole, from before you start pulling out the balls in the particular draw, any list of numbers you pick is equally likely.  So you can pick 1, 2, 3, 4, 5, 6.  You can pick random numbers like 12, 37, 14, or other random numbers - every single string of numbers has exactly the same chance of coming up.  What you're saying now is, once you start drawing the balls out, how does the probability change?  What people often forget with things in probability because as humans, we love to assign meaning and pattern to things, is that if you draw out one number, it doesnít change the odds of the next number at all, other than you can't draw the previous number that just came out.  So actually, your odds aren't going to change as you're drawing those numbers out as you go along.

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