Question

1. An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the Asian project is successful and B be the event that the European project is successful. Suppose that A and B are independent events with P(A) = 0.9 and P(B) = 0.5.

a) If the Asian project is not successful, what is the probability that the European project is also not successful?

Explain your reasoning.

Since the events are independent, then A' and B' are not independent.

Since the events are not independent, then A' and B' are mutually exclusive.

Since the events are independent, then A' and B' are independent.

Since the events are independent, then A' and B' are mutually exclusive.

(b) What is the probability that at least one of the two projects will be successful?

(c) Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful? (Round your answer to three decimal places.)

2. An insurance company offers four different deductible levels—none, low, medium, and high—for its homeowner's policyholders and three different levels—low, medium, and high—for its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance. For example, the proportion of individuals with both low homeowner's deductible and low auto deductible is 0.08 (8% of all such individuals).

	Homeowner's
Auto	N	L	M	H
L	0.04	0.08	0.05	0.01
M	0.07	0.11	0.20	0.09
H	0.02	0.03	0.15	0.15

Suppose an individual having both types of policies is randomly selected.

(a) What is the probability that the individual has a medium auto deductible and a high homeowner's deductible?


(b) What is the probability that the individual has a low auto deductible? A low homeowner's deductible?

auto deductible
homeowner's deductible

(c) What is the probability that the individual is in the same category for both auto and homeowner's deductibles?


(d) Based on your answer in part (c), what is the probability that the two categories are different?


(e) What is the probability that the individual has at least one low deductible level?


(f) Using the answer in part (e), what is the probability that neither deductible level is low?

Answer 1