Chapter 13.5, Problem 65STP

To determine

To find : Probability of rolling three $3$ 's, when cube is rolled three times.

Answer to Problem 65STP

(A)

Explanation of Solution

Given information :

Cube is rolled three times, cube has $6$ six faces, numbered $1,2,3,4,5,6$ one number on one face.

Calculation :

A cube is rolled $3$ times, cube has $6$ faces then $n(6)=6$ .

Probability of getting $3$ on firs roll = $\frac{\text{1}}{\text{6}}$

On second roll = $\frac{\text{1}}{\text{6}}$

On third roll = $\frac{\text{1}}{\text{6}}$

All events are independent,

Then p(getting three on all $3$ rolls) $=\frac{1}{6}\cdot \frac{1}{6}\cdot \frac{1}{6}=\frac{1}{216}$

Option (A).