Teens, Use of Social Media . We saw in Example 13.8 that 95% of teenagers are on

Question

Teens, Use of Social Media. We saw in Example 13.8 that 95% of teenagers are online, and that 81% of online teens use some kind of social media. Of online teens who use some kind of social media, 91% have posted a photo of themselves. What percent of all teens are online, use social media, and have posted a photo of themselves? Define events and probabilities, and follow the pattern of Example 13.9.

EXAMPLE 13.8 Teens Use of Social Media The Pew Internet and American Life Project finds that 95% of teenagers aged 12 to 17) use the Internet, and that 81% of online teens use some kind of social media·6 What percent of teens are online and use some kind of social media? Use the multiplication rule: P(online) = 0.95 Pluse social media | online) 0.81 P(online and use social media)-P(online) × P(use social media | online) (0.95)(0.81) 0.7695 That is, about 77% of all teens are online and use some kind of social media. You should think your way through this: if 95% of teens are online and 81% of these use some kind of social media, then 81% of 95% are both online and use some kind of social media. It is important to remember that the conditional probability of an event generally depends on the event we condition on. Although we have shown P (use social media online) 0.81, since someone who is not online cannot be using social media, we have Pluse social media l not online) = 0.

Explanation / Answer

Let

O = {a teenager is online}
S = {a teenager uses social media}
P = {a teenager posts of photo of himself}

Hence,

P(O) = 0.95
P(S|O) = 0.81
P(P|S n O) = 0.91

Hence, by multiplication rule,

P(O n S n P) = P(O) P(S|O) P(P|S n O) = 0.95*0.81*0.91

= 0.700245

= 70.0245% [ANSWER]

Hence, around 70.0245% of teens are online, use social media, and have posted a photo of themselves.

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