Question

the odds of rolling a certain number on a single die is 1 chance in 6 rolls. in course of a game, someone rolled 3 fives. according to the odds, how many times must that person have thrown the die

Answer 1

18

Explanation:

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 have 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 likely number of rolls needed to get three 5's.