PROBLEM SOLVING ON CONDITIONAL PROBABILITY AND PRODUCT RULE

Answer carefully and show your complete solution.

1. A hospital is testing patients for a certain disease. If a patient has the disease, the test is designed to return a "positive" result. If a patient does not have the disease, the test should return a "negative" result. No test is perfect though.

?99% of patients who have the disease will test positive.

?5% of the patients who don't have the disease will also test positive.

?10% of the population in question has the disease.

If a random patient tests positive, what is the probability that they have the disease?

a. Find the probability that a randomly selected patient has the disease AND tests positive ?

b. Find the probability that a random patient tests positive.

c. If a random patient tests positive, what is the probability that they have the disease?

2. Researchers surveyed recent graduates of two different universities about their annual incomes. The following two-way table displays data for the 300 graduates who responded to the survey:

Annual University A University B TOTAL Income(USD) Under 20,000 36 24 60 20,000 to 109 56 165 39,999 40,000 and over 35 40 75 TOTAL 180 120 300