If a fair die is rolled 5 times, what is the probability, to the nearest thousandth, of getting exactly 0 twos?

Answer 1

If we break each roll of the die into two outcomes: 1) rolling a two (P = 1/6) and 2) not rolling a two (P = 5/6) then we can see that each roll (5 of them) has the same probabilities. So "not rolling a two", 5 times, (aka , rolling exactly zero twos) would yield a probability of (5/6) • (5/6) • (5/6) • (5/6) • (5/6) which is 5⁵/6⁵ = 0.402