Question

A fair die is rolled 4 times. What is the probability that a 4 is obtained on at least one of the rolls? Round your answer to three decimal places.

Answer 1

The easiest way to do this problem is to look a the probability that you will NOT get a 4.

On the first roll, the probability of not getting a 4 is 5/6.
The probability is the same for each of the 2nd, 3rd, and 4th rolls.

Each roll is independent of the others, so the probability of not getting a 4 in 4 rolls is
\[\frac{5^4}{6^4}\]
However, you want the probability of getting a 4, which is can be represented as 100% minus the probability of a failure, or
\[1-\frac{5^4}{6^4}\]

Answer 2

Thanks!

Answer 3

Sure thing :)