A fair die is rolled fourfour times. A 2 is considered "success," while all other outcomes are "failures." Find the probability of 4 successessuccesses.
Accepted Solution
A:
Answer:Hence, the probability is: [tex]\dfrac{1}{6^4}\ or\ 0.000772[/tex]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:[tex]=\dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{1}{6}\\\\\\\\=\dfrac{1}{6^4}\\\\\\=0.000772[/tex]