Five draws with replacement

Topic: Random variables and distributions · more questions on this topic
‹ Distance to the centre Five draws without replacement ›

Five numbers are drawn with replacement from \{1,\ldots,100\}, each draw independent and uniform. Find the probability that exactly three of the five numbers are even.

Worked answer (click to show)

Each draw is even with probability 1/2, independently. The number of evens is \operatorname{Bin}(5,1/2), and \mathbb{P}(X=3)=\binom{5}{3}/32=5/16.