Couple of days ago there were two lottery draws in my country. Two consecutive results in a Lottery(6/90) are as given:
-8 22 50 55 71 87
-8 22 42 52 55 71
As it is seen 4 numbers are the same in both draws and as announced, it is 1 in a 5,437,710,000,000.
However, would it not be the same probability for any two consecutive draws?
For example:
-16 43 64 73 85 88
-7 8 39 55 61 72
If you predict that the next two draws will be "8 22 50 55 71 87" and "8 22 42 52 55 71", then the probability that you are right is very low. It doesn't matter which numbers you pick, the probability remains the same. You are betting on a single outcome.
If you say instead: "the next two consecutive draws will have 4 numbers in common!", then there are many outcomes for which this is true, so the chance that you are right is higher.
To calculate the exact chance, you divide the number of combinations for which you are right by the total number of possible combinations. (This works only when all combinations are equally likely, e.g. for exact dice combinations or lottery outcomes.)