Ann throws a dice 30 times. The chances of getting 1, 2, 3, 4, 5 or 6 are equal.
a. How big of a chance is there that her next throw will be a 3?
b. Ann throws the dice another 12 times. How many times is she expected to throw a 3 on these 12 throws?
a. 1 / 6 Previouse results have no effect on the probability of the next throw.*
b. 2 / 6 I think the word "expected" is inappropriate.
Instead, say "the probability" of throwing another 3.
* You might be tempted to say, "Well, that darn three will never come."
Alternatively, "Well, the three hasn't come up, It's due any time now."
These fallacious conclusions are one way casinos make their money.
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