Question

A dice is rolled twice. Find the probability that (i) 5 will not come up either time. (ii) 5 will
come up exactly one time.

Answer 1

Total event $=6\times 6=36$

Events of getting $5$ are $=(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(1,5),(2,5),(3,5),(4,5),(6,5)$

probability of getting getting $5=\frac{11}{36}$

Probability of not getting $5=1-\frac{11}{36}=\frac{25}{36}$

probability of getting $5$ exactly one time is $=\frac{10}{36}$