12. Marginal, joint, and conditional probabilities based on a cross-classification table

Surveys conducted for the Pew Internet & American Life Project suggest that communication patterns vary across three groups of teenagers: social networkers, content creators, and multichannel teens (teens who use the Internet, instant messaging, text-messaging cell phones, and social networks).

In one survey, Internet-using teenagers were asked how often they send e-mail to friends. Their responses are summarized in the following table. Separate tabulations are provided for social networkers (teens who have a profile on a social network site such as Facebook or Instagram) and for teens who are not social networkers.

	E-mails Every Day	Does Not E-mail Every Day	Total
Social networker	104	389	493
Not a social networker	28	365	393
Total	132	754	886

Let S	=	the event the Internet-using teen is a social networker,
N	=	the event the Internet-using teen is not a social networker,
E	=	the event the Internet-using teen sends e-mail to friends every day, and
O	=	the event the Internet-using teen does not send e-mail to friends every day.

Consider this experiment: An Internet-using teenager is randomly selected and surveyed. The teen is categorized as a social networker or not a social networker and as someone who sends e-mail to friends every day or someone who does not.

The probability that the randomly selected Internet-using teenager does not send e-mail to friends every day is = .

The probability that the randomly selected Internet-using teenager is a social networker who does not send e-mail to friends every day is = .

The probability that the randomly selected Internet-using teenager does not send e-mail to friends every day given that he or she is a social networker is = .

Are events O and S independent?

Yes

No