Heres how I see it:-
Ok, I think PAB has answered Bertils first question correctly for the case when you are asking the question "What is the probability of
one, or a combination of n of the numbers in this five ball result repeating to another result ? Note that no specific ball is identified here, and for a single ball - its just any one of the five repeating.
So if the last result was 13,22,28,40,59 and you are asking for the probability of
one of
either 13,22,28,40,59 turning up in the next draw, then thats a single repeat and its probability (using PAB's figures) is 31.58%
This is true of comparison between
any two draws be they consecutive, 100 draws apart, or a million draws apart.
Bertil then asked " Do these data apply to the same ball repeating or any ball?". As I said they apply to any
unidentified combination of balls from the set of 5 repeating.
If you want to know the probability of a
specific ball from a set of 5 balls in past result repeating then thats different. I think its exactly the same as the probability of a single named ball (from the full range) being drawn next time - as the lottery has no memory and all balls have an equal chance. In a 5/59 game if you had asked whats the probability of number 22 being drawn (hence repeating by coincidence) then I suggest that you have five chances of it being drawn from the 59 available balls. that gives a probability of 5/59 = 8.47% exactly the same as any other number.
Your next question was :- Finally, what is the probability that one number would repeat three or more times from draw to draw? Well the old chestnut question about coin tosses can help here.
What is the probability that when you toss a coin that it will land heads three times in a row ? Well theres one answer, but there are 2 questions involved. The probability of heads in a single toss is 0.5, but the probability of getting heads
three times in a row is 0.5x0.5x0.5 =0.125. However the probability of getting heads at any stage and in the fourth toss is still 0.5 because each toss is independent, there is no memory trail determining outcome.
So, back to the lottery the probability of your named ball coming out
three times in a row is 0.0847 x0.0847 x0.0847 = 0.000609 or 0.06%. Remember the probability of it being drawn in
any draw, regardless of what went before is still 0.0847.
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