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

Answer 1

When you roll a die, each roll is "Independent" of the other rolls of the die.

To determine the probability of a die rolled 5 times and getting exactly 0 two's,

you would determine the probability of the die not rolling a two and multiply that value by itself 5 times.

Probably= favorable outcomes / possible outcomes

The possible outcomes of rolling a fair die are {1,2,3,4,5,6} = 6

The possible favorable or "desired" outcomes of not rolling a two {1,3,4,5,6} = 5

So the probability of not rolling a 2 with one roll is: 5/6

To determine the probability of doing this 5 times: (5/6) x (5/6) x (5/6) x (5/6) x (5/6) = (3125/7776)

= 0.401877572.. Rounding to the nearest thousandth is 0.402