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?

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

2x+15=33

Step-by-step explanation:

Let n be the number of days he has been doing sit ups, not counting the first day. Since he does 2 more sit-ups for each day, then the number of additional sit-ups is 2n.

Since he started doing  15 sit-ups on the first day, the total number of sit-ups

after x days would be 2n+15.

Since he did a total of 33 sit ups today, then 2n+15=33