A fair six-faced dice, with the faces labelled 1', 2', 3', 4', 5', 6', and V, is rolled thrice. What is the probability ...

Question

A fair six-faced dice, with the faces labelled 1', 2', 3', 4', 5', 6', and V, is rolled thrice. What is the probability of rolling V exactly once?

A. 25/72
B. 5/18
C. 25/216
D. 5/72

Accepted Answer

P(V exactly once in 3 rolls) = C(3,1) * (1/6) * (5/6)^2 = 75/216 = 25/72. A six-faced die is labeled with six values, one of which is V. So P(V) = 1/6 and P(not V) = 5/6 on each roll. The die is rolled three times independently. We want the probability that V appears on exactly one of the three rolls. This is a binomial probability with n = 3 trials and p = 1/6.

A fair six-faced dice, with the faces labelled 1', 2', 3', 4', 5', 6', and V, is rolled thrice. What is the probability of rolling V exactly once? A. 25/72 B. 5/18 C. 25/216 D. 5/72