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kerrichen
May 22nd 2005, 11:33 AM
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?

krzysio
May 22nd 2005, 11:51 AM
Independent is entirely different than mutually exclusive. When they are mutually exclusive, probability of intersection is zero.

In fact, you should remember that the concepts of:

Independence

and

Mutually Exclusive

are in fact

Mutually Exclusive. The only way mutually exclusive events can be independent only if one of them has probability zero.

Yours,
Krzys' Ostaszewski

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?