Financial Risk Manager Part 1
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A certain insurer sells two policies: homeowner's and life insurance. 60% of the insurer's customers holds homeowner's or life insurance policy. 40% have a homeowner's policy and 35% have a life insurance policy. What is the probability that a customer holds both insurance policies?
Other
Community
NNikitesh
A
5%
B
10%
C
15%
D
65%
Explanation:
Using the probability formula for the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Given:
- P(A ∪ B) = 60% = 0.60 (customers holding homeowner's OR life insurance)
- P(A) = 40% = 0.40 (customers holding homeowner's insurance)
- P(B) = 35% = 0.35 (customers holding life insurance)
Substituting into the formula: 0.60 = 0.40 + 0.35 - P(A ∩ B) 0.60 = 0.75 - P(A ∩ B) P(A ∩ B) = 0.75 - 0.60 P(A ∩ B) = 0.15 = 15%
Therefore, the probability that a customer holds both insurance policies is 15%.
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