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Category:Indian drama filmsWhat is the probability that the first three dice will come up an even number?
In a party game, three dice are rolled three times. If the first three rolls are even, what is the probability that the first three rolls will come up even?
This is a paradox because the probability of an even number rolling three times is $ rac{1}{6} $ since we can only roll even numbers. However if we calculate the probability of rolling an even number in any given roll we would get $ rac{1}{6} $.
How is this paradox resolved?
I would like to know how this question is resolved. I think there is a mistake in the question. I want to know what the true problem is.
The problem is the claim that the probability of an even number appearing on three rolls of three dice is $ rac{1}{6}$. This is clearly wrong, because the probability of a three-number sequence of any length is $ rac{1}{6^n}$ for $n$-numbered dice. There are three possible outcomes for the first roll: even-odd-even, odd-even-even, or even-even-odd. Then the probability of an even-even-even sequence is $ rac{1}{6}$, since there are two even outcomes and two odd. The chance of this is $ rac{2}{3} imes rac{1}{6} imes rac{1}{6}$. If the odds be359ba680
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