Ninsurance 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.

Step-by-step explanation:

First we can define some notation useful:

C ="represent the event of incurring in operating charges"

R= represent the event of emergency rooms charges"

For this case we are interested on P(C) since they want "the probability that a claim submitted to the insurance company includes operating room charges."

We have some probabilities given:

Solution to the problem

By the complement rule we have this:

Since the two events C and R are considered independent we have this:

Now we can use the total probability rule like this:

And if we replace we got: