Chapter 12.8, Problem 32PPE

To determine

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

Answer to Problem 32PPE

The required probability is $\frac{1}{12}$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Find the probability that 3 of 9 coins are a dime.

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

Find the probability that 2 of the 8 remaining coins are dime.

  $P\left(\text{dime}\right)=\frac{2}{8}$

Find the required probability as follows.

  $\begin{array}{c}P\left(\text{dime}\text{then}\text{dime}\right)=P\left(\text{dime}\right)\times P\left(\text{dime}\right)\\ =\frac{3}{9}\times \frac{2}{8}\\ =\frac{1}{12}\end{array}$

Therefore, the required probability is $\frac{1}{12}$ .