Worksheet #5: Compound Probability, General Multiplication Rule & Tree Diagrams Name_____________________________________________ 1. 45% of the Walton High School student body are male. 80% of Walton females love math, while only 60% of the males love math. What percentage of the student body love math? 2. Laptop computers are shipped to a university bookstore from three factories, A, B, and C. You know that factory A produces 20% defective laptops, whereas B produces 10% defectives and C only 5% defectives. The manager in the store receives a new shipment of laptops and discovers that 40% are from factory C, 40% are from factory B, and 20% are from factory A. (a) What is the probability of finding a defective laptop in this shipment? (b) Are the events “laptop comes from factory A” and “laptop comes from factory B” mutually exclusive? Are they independent? (c) Suppose the manager randomly selects one laptop and discovers that it is defective. What is the probability that it came from factory A? 3. Parking for students at Walton is very limited, and those who arrive late have to park illegally and take their chances at getting a ticket. Joey has determined that the probability that he has to park illegally and that he gets a parking ticket is .07. He has kept data from last year and found that because of his perpetual tardiness, the probability that he will have to park illegally is .25. Suppose that he arrived late once again this morning and had to park in a no-parking zone. Find the probability that Joey will get a parking ticket. 4. Heart disease is the #1 killer today. Suppose that 8% of the patients in a small town are known to have heart disease. And suppose that a test is available that is positive in 96% of the patients with heart disease, but is also positive in 7% of patients who do not have heart disease. If a person is selected at random and given the test and it comes out positive, what is the probability that the person actually has heart disease? 5. A laboratory test for the detection of a certain disease gives a positive result 5 percent of the time for people who do not have the disease. The test gives a negative result 0.3 percent of the time for people who have the disease. Large-scale studies have shown that the disease occurs in about 2 percent of the population. (a) What is the probability that a person selected at random would test positive for this disease? (b) What is the probability of a person selected at random who tests positive for the disease does not have the disease? Worksheet #5: Compound Probability, General Multiplication Rule & Tree Diagrams 6. Over time, a student analyzes her ability to guess correctly after narrowing down multiple choice answers in a 5-selection question. She discovers that if she narrows her answer set to 2 or 3 choices, her probability of getting the right answer is 0.8, but if she still has 4 or 5 choices left, her probability of choosing correctly decreases drastically to 0.1. Assuming that in general she can narrow her choices to 2-3 choices 70% of the time, what is the probability that she will answer a question correctly any time she must guess? Justify your answer. MULTIPLE CHOICE PRACTICE 7. For the tree diagram pictured below: X 0.3 0.4 A Y 0.8 0.3 Z X 0.5 0.2 0.4 Y B 0.1 What is P  B X  ? (a) 1/4 (b) 5/17 Z (c) 2/5 (d) 1/3 (e) 4/5 8. On a recent administration of a state bar exam, 22% of the test takers passed the test, 78% of those who passed were first-time test takers, and 60% of those who failed were first-time test takers. What percent of first-time test takers passed the test? (a) 17% (b) 27% (c) 47% (d) 64% (e) 73%