Question

Free downloads? Illegal music downloading is a big problem: 29% of Internet users download music files, and 67% of downloaders say they don’t care if the music is copyrighted. 18 Find the probability that a randomly selected Internet user downloads music and doesn’t care if it’s copyrighted.

Short answer

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

Step-by-step solution

Step 1:Given information

Music files are downloaded by 29% of Internet users.

67 $\%$of downloaders think it doesn't matter if the music is protected by copyright.

Step 2:Calculaton

According to general multiplication rule,

$P(\mathrm{A}\text{and}\mathrm{B})=P(\mathrm{A}\cap \mathrm{B})=P(\mathrm{A})\times P(\mathrm{B}\mid \mathrm{A})=P(\mathrm{B})\times P(\mathrm{A}\mid \mathrm{B})$

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,

$P\left(\mathrm{D}\right)=0.29$

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

$P(C\mid D)=0.67$

Apply the general multiplication rule:

$P\left(\mathrm{C}\text{and}\mathrm{D}\right)=P(\mathrm{C}\cap \mathrm{D})=P\left(\mathrm{D}\right)\times P(\mathrm{C}\mid \mathrm{D})$

$=0.29\times 0.67$

$=0.1943$

Thus

Probability for the randomly selected internet user downloads music and doesn't care about copyrighted music is$=0.1943$