5.3 Exercise 7 — Applied Probability

A real estate agent in a neighborhood heavily populated by affluent professional persons is working with a customer. The agent is trying to assess the likelihood the customer will actually buy. His experience indicates the following: if H is the event the customer buys, S is the event the customer is a professional with good income, and E is the event the customer drives a prestigious car, then

P \left(S\right) = 0 . 7 P \left(\right. S \left|\right. H \left.\right) = 0 . 90 P \left(\right. S \left|\right. H^{c} \left.\right) = 0 . 2 P \left(\right. E \left|\right. S \left.\right) = 0 . 95 P \left(\right. E \left|\right. S^{c} \left.\right) = 0 . 25

Since buying a house and owning a prestigious car are not related for a given owner, it seems reasonable to suppose $P \left(\right. E \left|\right. H S \left.\right) = P \left(\right. E \left|\right. H^{c} S \left.\right)$ and $P \left(\right. E \left|\right. H S^{c} \left.\right) = P \left(\right. E \left|\right. H^{c} S^{c} \left.\right)$ . The customer drives a Cadillac. What are the odds he will buy a house?

Pfeiffer, Applied Probability, 5.3 Problems on Conditional Independence, exercise 7

AI Tutor