Chapter 7.2, Problem 59PPS

Solution

a.

To calculate: Write expression to represent the probability of rolling a die ‘d’ times and getting a 3 each time.

  ${(\frac{1}{6})}^d$

Given information: The probability of rolling a die and getting a 3 is $\frac{1}{6}$ . And if we roll die twice, the probability of getting 3 both times is 1/6 times 1/6 or ${(\frac{1}{6})}^2$ .

Explanation:

If we roll the die for‘d’ times, we get the probability as $\frac{1}{6}*\frac{1}{6}*\frac{1}{6}*\mathrm{...}$ …. For d times

To write it in exponent form it is ${(\frac{1}{6})}^d$

b.

To calculate: We need to write the ${(\frac{1}{6})}^d$ as power of 6.

  $6^{-d}$

Given information: ${(\frac{1}{6})}^d$

Formula: Let’s use exponent rule $\frac{1}{a^m}=a^{-m}$

Explanation:

Using the exponent rule, we can rewrite ${(\frac{1}{6})}^d=\frac{1}{6^d}=6^{-d}$