[Math] If an ordinary six-sided die is thrown four times, find the probability of obtaining two even numbers and two odd numbers.

Question

An ordinary die is has six faces numbered from 1 to 6. If an ordinary die is thrown four times, find the probability of obtaining two even numbers and two odd numbers.

Answer 1

There are two outcomes with equal probability, so you want to divide combination $\binom{4}{2}=6$ (these are the cases you want) to the number of all possible outcomes (even or odd) which is $2^4$. So 6/16 should be the answer.