Chapter 11.3, Problem 17PPSE

Solution

To identify: Theprobability that you grab a novel both days.Reading Suppose you have five books in your book bag. Three are novels, one is a biography, and one is a poetry book. Today you grab one book out of your bag without looking, and return it later. Tomorrow you do the same thing.

The probability is $P\left(novel,novel\right)=\frac{9}{25}$

Given information:

The given is there are total 5 books, 3 novels, 1 biography and 1 poetry book.

Explanation:

Consider the information.

If have to grab a book on two days.

So, probability that on first day we get a novel is

  $P\left(novel\right)=\frac{3}{5}$

Probability that second day and get a novel is when novel grabbed on first day is returned again to the bag is:

  $P\left(novel\right)=\frac{3}{5}$

Both the events are independent events as grabbing novel on first day has no effect on second day as it is returned again to the bag.

For independent events

  $P\left(AandB\right)=P\left(A\right)\cdot P\left(B\right)$

So,

  $\begin{array}{l}P\left(novel,novel\right)=\frac{3}{5}\cdot \frac{3}{5}\\ P\left(novel,novel\right)=\frac{9}{25}\end{array}$

Hence $P\left(novel,novel\right)=\frac{9}{25}$