Chapter 12.6, Problem 37S

To determine

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

Answer to Problem 37S

The expression for probability of rolling a die n times and getting a prime number n times is $\frac{1}{2^n}$

Explanation of Solution

Given information:

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

Calculation:

The probability of rolling a die and getting a prime number $=\frac{3}{6}=\frac{1}{2}$

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

The probability of rolling a die three times and getting a prime number three times $\text{=}\frac{1}{2}\cdot \frac{1}{2}\cdot \frac{1}{2}=\frac{1}{2^3}$

Similarly,

The probability of rolling a die n times and getting a prime number n times $=\frac{1}{2^n}$