Chapter 5.3, Problem 77E

To determine

Probability for the randomly selected internet user downloads music and doesn’t care about copyrighted music.

Answer to Problem 77E

Probability for the randomly selected internet user downloads music and doesn’t care about copyrighted music is 0.1943.

Explanation of Solution

Given information:

29% of the Internet users download music files.

67% of the downloaders say they don’t care if the music is copyrighted.

Calculations:

According to general multiplication rule,

  $P\left(\text{A}\text{and}\text{B}\right)=P\left(\text{A}\cap \text{B}\right)=P\left(\text{A}\right)\times P\left(\text{B}|\text{A}\right)=P\left(\text{B}\right)\times P\left(\text{A}|\text{B}\right)$

Let

D: Internet users download music files

C: Downloaders don’t care about copyrighted music

Now,

The corresponding probabilities:

Probability for the internet users download music files,

  $P\left(\text{D}\right)=0.29$

Probability for the downloaders don’t care about copyrighted music,

  $P\left(\text{C}|\text{D}\right)=0.67$

Apply the general multiplication rule:

  $\begin{array}{l}P\left(\text{C}\text{and}\text{D}\right)=P\left(\text{C}\cap \text{D}\right)=P\left(\text{D}\right)\times P\left(\text{C}|\text{D}\right)\\ =0.29\times 0.67\\ =0.1943\end{array}$

Thus,

Probability that a randomly selected Internet user downloads music and doesn’t care if it’s copyrighted is 0.1943.