Probabilities Question independent events

60 Views Asked by At

There is a question as below : 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 consists only of operating room charges.

Let operation room be $O$ and emergency be $E$.

$P(O) = 0.40$, which is the answer.

The question is doesn't the phrase "consists only of operating room charges" mean $P(O)-P(O)\cdot P(E)$? Why then say that $Pr(O)$ is the answer?