The roll is bigger than two, is it odd?

Question

You roll one fair six-sided die out of sight. A friend looks and tells you the result is greater than two. Given that, what is the probability the result is odd?

Accepted Answer

"Greater than two" leaves the outcomes: \{3,\ 4,\ 5,\ 6\}, which are four equally likely results. Among them, the odd numbers are 3 and 5, so two qualify: P(	ext{odd} \mid 2) = \frac{2}{4} = \frac{1}{2}. Within this reduced set the odd and even results happen to be balanced (3,5 against 4,6), so it is an even chance. Takeaway. Always recount odds versus evens inside the conditioned set rather than assuming the original one-half still holds; here it does, but only by coincidence of the counts.

The roll is bigger than two, is it odd?

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