Five draws without replacement

Topic: Random variables and distributions · more questions on this topic
‹ Five draws with replacement Particles in an hour ›

Five numbers are drawn without replacement from \{1,\ldots,100\}. Find the probability that exactly three of them are even.

Worked answer (click to show)

The draw is hypergeometric: 5 items from 100, of which 50 are even.

\mathbb{P}(X=3)=\frac{\binom{50}{3}\binom{50}{2}}{\binom{100}{5}}\approx 0.319.