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BAYES’ THEOREM Conditional probability takes into account information about the occurrence of one event to predict the probability of another event. This concept can be extended to “revise” probabilities based on new information and to determine the probability that a particular effect was due to specific cause. The procedure for revising these probabilities is known as Bayes’ Theorem. P(B) P(A| B) P(B| A) = P(A) Sample Problems: 1. An advertising executive is studying television viewing habits of married men and women during prime-time hours. Based on past viewing records, he has determined that during prime time husbands are watching television 60% of the time. It has also been determined that 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 a) If the wife is watching television, the husband is also watching television. b) The wife is watching television during prime time. 2. A television station would like to measure the ability of its weather forecaster. Past data have been collected that indicate the following: a) The probability the forecaster predicted sunshine on sunny days is 0.80. b) The probability the forecaster predicted sunshine on rainy days is 0.40. c) The probability of a sunny day is 0.60. Find the probability that (a) It will be sunny given that the forecaster has predicted sunshine. (b) The forecaster will predict sunshine. 3. The Olive Construction Company is determining whether it should submit a bid for a new shopping center. In the past, Olive’s main competitor, Base Construction Company, has submitted bids 70% of the time. If Base Construction Company does not bid on a job, the probability that the Olive Construction Company will get the job is 0.50. If Base Construction Company does bid on a job, the probability that the Olive Construction Company will get the job is 0.25. (a) If the Olive Construction Company gets the job, what is the probability that the Base Construction Company did not bid? (b) What is the probability that the Olive Construction Company will get the job? BAYES’ THEOREM.doc last corrected on 6/19/2000