Chapter 12.6, Problem 36S

To determine

To write an expression to represent the probability of rolling a die ntimes and getting 3 n times.

Answer to Problem 36S

The expression for probability of rolling a die n times and getting 3n times is $\frac{1}{6^n}$

Explanation of Solution

Given information:

The expression should represent the probability of rolling a die n times and getting 3 n times as a power of 6.

Calculation:

The probability of rolling a die and getting 3 $=\frac{1}{6}$

The probability of rolling a die two times and getting 3 two times $=\frac{1}{6}\cdot \frac{1}{6}=\frac{1}{6^2}$

The probability of rolling a die three times and getting 3 three times $\text{=}\frac{1}{6}\cdot \frac{1}{6}\cdot \frac{1}{6}=\frac{1}{6^3}$

Similarly,

The probability of rolling a die ntimes and getting 3n times $=\frac{1}{6^n}$