Question

Brett and Margo have each thought about murdering their rich Uncle Basil in hopes of claiming their inheritance a bit early. Hoping to take advantage of Basil’s predilection for immoderate desserts, Brett has put rat poison into the cherries flamb´ e; Margo, unaware of Brett’s activities, has laced the chocolate mousse with cyanide. Given the amounts likely to be eaten, the probability of the rat poison being fatal is 0.60; the cyanide, 0.90. Based on other dinners where Basil was presented with the same dessert options, we can assume that he has a 50% chance of asking for the cherries flambe, a 40% chance of ordering the chocolate mousse, and a 10% chance of skipping dessert altogether. No sooner arc the dishes cleared away than Basil drops dead. In the absence of any other evidence, who should be considered the prime suspect?

Answer 1

Answer:

Step-by-step explanation:

The probability of asking for the cherries flambe and dying, P(A) = 0.5 × 0.6 = 0.3

The probability of asking for the chocolate mousse and dying, P(A) = 0.4 × 0.9 = 0.36

The probability of skipping dessert altogether = 0.1 × 0 = 0

The probability that the rich uncle dies, P(D) is

P(D) = 0.3 + 0.36 + 0 = 0.66

To determine the prime suspect, we would apply the concept of conditional probability. It is the probability of an event, A occurring given that event B has occurred. We would compare probabilities of the events A and B occurring given that event D also occurred

Therefore,

P(A|D) = 0.3/0.66 = 0.45

P(B|D) = 0.36/0.66 = 0.55

Therefore, the prime suspect is Margo because his probability is higher