Your favorite team is in the final playoffs. You have assigned a probability of

Question

Your favorite team is in the final playoffs. You have assigned a probability of 60% that it will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 70% of the time. When they lose the series, they win the first game 25% of the time. The first game is over; your team has lost. What is the probability that it will win the series? The Rapid Test is used to determine whether someone has HIV (the virus that causes AIDS). The false-positive and false-negative rates are .027 and .080, respectively. A physician has just received the Rapid Test report that his patient tested positive. Before receiving the result, the physician assigned his patient to the low-risk group (defined on the basis of several variables) with only a 0.5% probability of having HIV. What is the probability that the patient actually has HIV?

Explanation / Answer

6.81

Probabilit that it will win the series = 0.60 * 0.70 + (1-0.70)*0.25

Probability = 0.495

6.93

Probability that actually has HIV = 0.005 * 0.027 + (1-0.005) * 0.080

Probability is = 0.079735

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