Chapter 12.5, Problem 3CYU

To determine

To state whether the probability is dependent or independent and find the probability.

Answer to Problem 3CYU

The events are independent and the probability of not choosing a dime is $\frac{4}{9}\text{ or 44}\text{.4\%}$ .

Explanation of Solution

Given information:

The given statement is:

“Nakos has $4$ quarters, $3$ dimes and $2$ nickels in his pocket. Nakos randomly picks two coins out of his pocket. What is the probability that he did not choose a dime either time, if he replaced the first coin choosing a second coin?”

Formula used:

The following formula is used:

  $\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Calculation :

The outcome of one event does not affects the outcome of the other because the coin is replaced, so they are independent events.

The probability that Nakos does not choosea dime either time can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{not a dime}\right)=\frac{6}{9}\\ \text{P}\left(\text{not a dime}\right)=\frac{6}{9}\\ \text{P}\left(\text{not a dime, not a dime}\right)=\frac{6}{9}\times \frac{6}{9}\\ \text{P}\left(\text{not a dime, not a dime}\right)=\frac{4}{9}\text{ or 44}\text{.4\%}\end{array}$

Hence, the events are independent and the probability of not choosing a dime is $\frac{4}{9}\text{ or 44}\text{.4\%}$ .