On the sample exam questions provided by SOA, on question #17, it is states as:

An insurance company pays hospital claims. The number of claims that include emergency room or operating room charges is 85% of the total number of claims. The number of claims that do not include emergency room charges is 25% of the total

number of claims. The occurrence of emergency room charges is independent of the occurrence of operating room charges on hospital claims.

Calculate the probability that a claim submitted to the insurance company includes

operating room charges.

(A) 0.10

(B) 0.20

(C) 0.25

(D) 0.40

(E) 0.80

The answer provided is 0.85=Pr(O U E) = Pr(O) + Pr(E) - Pr(O)Pr(E).

My questions is since O and E are independent, Pr(0)Pr(E) should be zero. Why is Pr(O)Pr(E) calculated as the answer?

Final answer is 0.4 instead of 0.1.

An insurance company pays hospital claims. The number of claims that include emergency room or operating room charges is 85% of the total number of claims. The number of claims that do not include emergency room charges is 25% of the total

number of claims. The occurrence of emergency room charges is independent of the occurrence of operating room charges on hospital claims.

Calculate the probability that a claim submitted to the insurance company includes

operating room charges.

(A) 0.10

(B) 0.20

(C) 0.25

(D) 0.40

(E) 0.80

The answer provided is 0.85=Pr(O U E) = Pr(O) + Pr(E) - Pr(O)Pr(E).

My questions is since O and E are independent, Pr(0)Pr(E) should be zero. Why is Pr(O)Pr(E) calculated as the answer?

Final answer is 0.4 instead of 0.1.

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