Question

11. Noree has a phone worth $60 and a tablet worth $240. The probability she'll have to replace the phone (because of damage/loss/theft/etc.) is 1/5. The probability she 'll have to replace the tablet is 1/6. These probabilities are independent се An insurance pol icv that costs $60 will cover the cost of replacing both items a. What is the expected monetary value of buying the insurance? b. What is the expected monetary value of declining the insurance?

Answer 1

We have p(phone replace) = p(p) = 1/5 p(tablet replace) = p(T) = 1/6 if she buys insurance, P(PT) = 1/5 1/6 (since both are independent) = 1/30 P(PT^bar) = 1/5 5/6 = 1/6 = 5/30 P(P^bar T) = 4/5 1/6 = 2/15 = 4/30 P(P^bar T^bar) = 4/5 5/6 = 4/6 = 20/30 now, she gets $ 300 if PT happens, i.e. with prob 1/30 $ 60 if PT^bar happens i.e. with prob 5/30 $ 240 with prob 4/30 and $0 with prob 20/30 and she has to pay $60 for insurance therefore expected monetary value of buying insurance is - 60 + 1/30(300) + 5/30(60) + 4/30(240) + 20/30(0) = -60 + 10 + 10 + 32 + 0 = -8, i.e. out go (expenditure) of $8 \r\n if she declines the insurance, she needs to pay $60 with prob 5/30 rightarrow PT^bar $240 with prob 4/30 rightarrow P^bar T