Question

A fair die is rolled fourfour times. A 2 is considered​ "success," while all other outcomes are​ "failures." Find the probability of 4 successessuccesses.

Answer 1

Answer:

Hence, the probability is:

            $\dfrac{1}{6^4}\ or\ 0.000772$

Step-by-step explanation:

It is given that:

A fair die is rolled four times. A 2 is considered​ "success," while all other outcomes are​ "failures."

This means that the probability of 4 successes is the outcome such that each of the four die will result in the outcome 2.

Also, the probability of 2 in each of the die is: 1/6

( since, there are total 6 outcomes in a die {1,2,3,4,5,6} and out of which there is only one '2' )

Also, we know that the outcome on one die is independent on the other this means that  the probability of 4 successes is:

$=\dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{1}{6}\\\\\\\\=\dfrac{1}{6^4}\\\\\\=0.000772$