Question

A dice is rolled twice. Find the probability that 5 will come up exactly one time   

Answer 1

The outcomes where 5 will come up exactly one time are

(1, 5), (2, 5), (3, 5), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (6, 5)
So, the number of favourable outcomes are 10.
∴ P(5 will come up exactly one time) = \[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{10}{36} = \frac{5}{18}\]