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What is the probability that a fair six-sided die lands on an even number three out of five times it is rolled?

For one roll, the outcomes are $1, 2, 3, 4, 5, 6$ of which $2, 4, 6$ are even, so the probability is $3/6=1/2$. But how to deal with "three out of five times" part?

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    $\begingroup$ It is the same as the probability that a fair coin will land heads three out of five times. $\endgroup$ – Igor Rivin Dec 12 '13 at 0:35
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Because the number of even sides are equal to odd sides, you can simplify the problem to "What is the probability that a coin lands on heads three times out of five?

For which the probability is $5$ pick $3$ out of $32$ or $$\frac{1}{32} \cdot \frac{5 \cdot 4 \cdot 3}{3\cdot 2 \cdot 1}=\frac{10}{32}= \frac{5}{16}.$$

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  • $\begingroup$ Oh dang I see. The 32 is from, 2 x 2 x 2 x 2 x 2? (5 tests and 2 possible outcomes?) $\endgroup$ – Asia x3 Dec 12 '13 at 0:53
  • $\begingroup$ Yes, it is. Good luck with probability! $\endgroup$ – Lily Dec 12 '13 at 1:36

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