The expected value is the probability times the frequency.
3 = 1/6 × n
n = 18
Note: the use of the word "odds" is very misleading here. Odds are the ratio of number of successes to number of failures:
S / F
Probability is the ratio of number of successes to number of all outcomes:
S / (S + F)
So the probability of rolling a 5 is 1/6. The odds of rolling a 5 is 1/5.
Furthermore, the word "must" is also incorrect. The player didn't <em>have</em> to roll 18 times. They could have rolled three times and gotten a 5 each time. Or they could have rolled 100 times. 18 is simply the most <em>likely </em>number of rolls needed to get three 5's.
