Drawing primes

If I draw 4 numbers without replacement from the first 16 primes, what is the probability the sum is even?

Solution

The only even prime is $2$. Thus the probability of not drawing $2$ is the probability the sum is even:

\(\mathrm{Pr}(\text{ sum is even }) = \frac{15}{16} \frac{14}{15} \frac{13}{14} \frac{12}{13} = \frac{3}{4}\)