A marketing executive is studying internet habits of married men and women durin

Question

A marketing executive is studying internet habits of married men and women during the 8am - 10pm period on weekends ("prime internet time"). Based on past data, he has determined that husbands are on the internet 10% of the time during prime internet time. It has also been determined that when the husband is on the internet during prime internet time, 40% of the time the wife is also on the internet. When the husband is not on the internet during prime internet time, the wife is on the internet 20% of the time. If the wife is on the internet during prime internet time, what is the probability that the husband is also on the internet?

Explanation / Answer

P(husband is on the internet) = 0.1

P(husband is not on the internet) = 1 - 0.1 = 0.9

P(wife is on the internet | husband is on the internet) = 0.4

P(wife is on the internet | husband is not on the internet) = 0.2

P(wife is on the internet) = P(wife is on the internet | husband is on the internet) * P(husband is on the internet) + P(wife is on the internet | husband is not on the internet) * P(husband is not on the internet)

                              = 0.4 * 0.1 + 0.2 * 0.9

                              = 0.22

P(husband is on the internet | wife is on the internet) = P(wife is on the internet | husband is on the internet) * P(husband is on the internet) / P(wife is on the internet)

                                                             = 0.4 * 0.1 / 0.22

                                                             = 0.1818

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