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

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?

• It is the same as the probability that a fair coin will land heads three out of five times. – Igor Rivin Dec 12 '13 at 0:35

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