Question

Teens online We saw in an earlier example (page 319) that 93% of teenagers are online and that 55% of online teens have posted a profile on a social-networking site. Of online teens with a profile, 76% have placed comments on a friend’s blog. What percent of all teens are online, have a profile, and comment on a friend’s blog? Show your work.

Short answer

The percentage of all online, have a profile, and comments on a friend’s blog is $38.874\%$

Step-by-step solution

Step 1. Given Information

$93\%$ of teenagers use the internet, and $55\%$ of them have created profiles on social networking sites.

Step 2. Concept Used

Conditional probability:$P(A\cap B)=P(A/B)\times P\left(B\right)$

Step 3. Calculation

According to the inquiry, $P\left(college\right)=93\%=0.93$

$$\begin{gathered} P(profile/online)=55\%=0.55 \\ P(comments/profile\cap online)=76\%=0.76 \end{gathered}$$

Use the following conditional probability definition:

$P(comments\cap profile\cap online)=P(comments/profile\cap online)\times P(profile/online)$

$$\begin{gathered} =P(comments/profile\cap online)\times P(profile/online)\times P\left(online\right) \\ =0.76\times 0.55\times 0.93=0.38874=38.874\% \end{gathered}$$

As a result, the following was obtained:

As a result, the percentage of people who are online, have a profile, and comment on a friend's blog is $38.874\%$