Chapter 12.8, Problem 26PPE

To determine

To find: The probability $P\left(\text{dime}\text{then}\text{nickel}\right)$ .

Answer to Problem 26PPE

The required probability is $\frac{1}{8}$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the probability that picked coin is dime.

  $P\left(\text{dime}\right)=\frac{3}{9}$

Find the probability that picked coin is nickel.

  $P\left(\text{nickel}\right)=\frac{3}{8}$

Find the required probability as follows.

  $\begin{array}{c}P\left(\text{dime}\text{then}\text{nickel}\right)=P\left(\text{dime}\right)\times P\left(\text{nickel}\right)\\ =\frac{3}{9}\times \frac{3}{8}\\ =\frac{1}{8}\end{array}$

Therefore, the required probability is $\frac{1}{8}$ .