A graphing calculator may be used wherever possible. However, you need to substa

Question

A graphing calculator may be used wherever possible. However, you need to substantiate your answers for full credit. If you run out of room for your response, use the back of the page. [1(8) An advertising executive is studying television viewing habits of married men and women during prime-time hours. Based on past viewing records, the executive has determined that during prime-time, husbands are watching television 60% of the time, when the husband is watching television, 40% of the time the wife is also watching, when the husband is not watching television, 30% of the time the wife is watching television. Find the probability that if the wife is watching television, the husband is also watching elevision.

Explanation / Answer

Let Probability of Husband watching = P(H) and Husband not watching = P(H')

Let Probability of Wife watching = P(W) and Wife not watching = P(W')

Given: P(H) = 0.6, P(H') = 1 - 0.6 = 0.4,

P(Wife is watching given Husband is Watching TV) = P(W/H) = 0.4 and

P(Wife is watching, given Husband is not watching) = P(W/H') = 0.3

To Find Probability of Husband watching, given that the wife is watching TV) = P(H/W)

By Bayes Theorem: P(H/W) = P(H) x P(W/H) / P(W)

P(W) = P(W/H) * P(H) + P(W/H') * P(H') = (0.4 * 0.6) + (0.3 * 0.4) = 0.24 + 0.12 = 0.36

Therefore P(H/W) = 0.6 * 0.4/0.36 = 24/36 = 2/3 = 0.67

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