Question

If you roll a fair die three times, what is the probability that you don't roll any 5's?

Answer 1

Pr {Not getting a '5' in throwing a die} = 5/6.
Pr{ One does not roll any '5' in three consecutive rolls of a die} = `(5/6)^3` = 125/216.

Explanation:

Here the events of throwing a number other than '5' in consecutive throws is independent. Hence probability is product of the probabilities namely (5/6) `xx` (5/6)`xx` (5/6) = 125/216.