Hello everyone : here's Jack's little story
So let's say the lotto Jack's playing is: $5$ numbers between $1$ and $49$
And let's say he likes to play : $ 28 , 13 , 35 , 41 , 8 $
I know that to win we have : $49 \times 48 \times 47 \times 46 \times 45 $ and we have $5!$ permutation …
Boom , he WON .
Jack says that he will not play with this combination anymore because he already won with it.
It's like winning with $1,2,3,4,5$ or $2,4,6,8.10$ , or also $5,10,15,20,25$ Jack says that we may have more chance to win with this combination because we never saw a draw like that.
I don't think he's right but I see what he meant by that
Are all these statements true?
Best Answer
Both of Jack's assertions are examples of the so-called gambler's fallacy, that an event which has happened more often in the past is less likely to happen in the future, or one which has happened less often in the past is more likely to happen in the future. This is a fallacy whenever (as with lotto draws) the event in question has the same probability of occurring regardless of what has happened in the past. For lotto draws which choose $5$ numbers out of $49$ without replacement there are $\ {49\choose5}=$$\frac{49!}{5!\,44!}\ $ equally likely possible combinations of $5$ numbers that can be drawn, so, if you have just one entry, your probability of winning is always $\ \frac{5!\,44!}{49!}\approx5.2\times10^{-7}\ $, regardless of what numbers you choose, or what numbers have ever been drawn in the past.