Chapter 12.5, Problem 4CYU

To determine

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

Answer to Problem 4CYU

The events are independent and the probability of selecting two math books is $\frac{64}{289}\text{ or 22}\text{.1\%}$ .

Explanation of Solution

Given information:

The given statement is:

“Joanna needs a book to prop up a table leg. She randomly selects a book, puts it back on the shelf, and selects another book. What is the probability that Joanna selected two math books?”

There are $4$ science books, $5$ history books and $8$ math books.

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 book is replaced, so they are independent events.

The probability that Joannaselected two math books can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{math}\right)=\frac{8}{17}\\ \text{P}\left(\text{math}\right)=\frac{8}{17}\\ \text{P}\left(\text{math, math}\right)=\frac{8}{17}\times \frac{8}{17}\\ \text{P}\left(\text{math, math}\right)=\frac{64}{289}\text{ or 22}\text{.1\%}\end{array}$

Hence, the events are independent and the probability of selecting two math books is $\frac{64}{289}\text{ or 22}\text{.1\%}$ .