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Once more, the BBC are utter dicks..
Lottery officials say that in 2002 Ms Wilson beat odds of 1 in 5.2 million when she won the Cool Million scratch card game

Then last month she beat odds of 1 in 705,600 by winning New York lottery's Jubilee scratch card game.


Experts say that the chances of her winning both games were an incredible 1 in 3,669,120,000,000.
So unbelievably wrong..

As anybody with a grasp on probability knows, the chance they've quoted is the chances of predicting "You will win the lottery on X date and Y date". Which is utter bullshit, that's not the way that maths works, or the way in which the layman understands probability.

What they want is the chance of her winning two $1m jackpots in the space of four years. Assuming she enters one competition per week, she has approximately 200 chances over the space of those four years. That cuts down the odds right away to nearer to one in about 30bn. And that's if we only consider these four years, and only if she buys one scratchcard per week. She's probably been buying them all her life, and probably bought more after she won the first $1m. Which makes it even more likely that she'd win twice in her life (which is what the layperson is really interested in - four years is just arbitrary).

I can't be bothered to go into the technicalities, I don't think they're important. The important thing is that once again, the BBC have got their story wrong, because it's more fun to look sensationalist than to look reasonable.

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Indeed, the statistic is correct, but reflects the probability of:

1. "Mrs X, you will win Lottery A on 01.07.2002 and Lottery B on 01.07.2006"

Now that's fine, but I'm betting those weren't the only times she's played the lottery in her life. A fairer probability would be for the following statement:

2. "Mrs X, at some point in your life you will win both Lotteries A and B"

Or even:

3. "Mrs X, in the 21st century you will win both Lotteries A and B within the space of five years"

The thing that made her newsworthy is not that she won those specific lotteries on those specific dates (for which the probability has been calculated), but that she won the lottery twice in her lifetime. The probability for the latter outcome is much higher (though still tiny, obviously).

Calculating absurdly impossible probabilities after the fact is the work of hacks and innumerates. It's like me tossing a coin fifty times, then proudly boasting that I 'beat odds' of one in a quadrillion to get that exact sequence of heads and tails. That's all very well, but probability works forwards, not backwards - it is used before something happens to indicate its likelihood. Which is why I don't think anybody would ever actually use statement 1 above. They would make one of the other statements, each of which has a much more favourable probability.

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