Hence, the probability is:
[tex]\dfrac{1}{6^4}\ or\ 0.000772[/tex]
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:
[tex]=\dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{1}{6}\\\\\\\\=\dfrac{1}{6^4}\\\\\\=0.000772[/tex]
