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Week 8 Homework, Part A

The greatest reward for a student is not a good grade. It is the willingness of his teacher to listen to him.

- Nikolay Konstantinov

Answer every question. Try being nice to your eyes and posture by printing this page and working with pencil and paper. Then use the button at the bottom of the page to create a code by processing your answers. Copy-and-paste the code into an e-mail along with the answer to your short answer question.

Keep trying each homework assignment until you get 8 out of 10 or more.

1. When rolling two dice, what is the probability of the sum being 8 or more? And what are the odds of the sum being 8 or more?

table showing the sum of two dice
14% and 5:31 42% and 15:21 58% and 15:21
14% and 5:36 42% and 15:36 58% and 15:36

Lyme disease is the leading tick-borne disease in the United States and Europe. Diagnosis is difficult and is aided by a test that detects particular antibodies in the blood. A study of 1,000 people at risk for Lyme disease showed the results of the blood test, sorted by whether or not the patient actually had Lyme disease. Use the table to answer the questions that follow.

Patient Has Lyme DiseasePatient Does Not Have Lyme Disease
Positive Test1910
false positive
Negative Test1
false negative
970

2. What percent of patients actually had Lyme disease?

2% 3% 20% 29% 80%

3. What percent of patients tested positive for Lyme disease?

2% 3% 20% 29% 80%

4. What percent of patients with Lyme disease tested positive? (This measures the test's accuracy.)

1.9% 19% 45% 66% 95%

5. Most of the time, we don't know whether a patient has Lyme disease or not. If a patient had a positive test result, what is the probability that the patient actually had Lyme disease?

1.9% 19% 45% 66% 95%

A restaurant surveyed customers about breakfast, asking them their favorite sandwich and their favorite beverage. Use the table to answer the questions that follow.

CheeseMeatPeanut Butter
Coffee391
Tea922
Hot Chocolate4714

6. What is the probability that a customer prefers a drink other than coffee?

34% 25% 26% 75%

7. What is the probability that a customer prefers a peanut butter sandwich and prefers coffee?

2% 6% 8% 57% 59%

8. What is the probability that a customer prefers a peanut butter sandwich or prefers coffee?

2% 6% 8% 57% 59%

9. What is the probability that a customer prefers a cheese sandwich and prefers tea?

18% 39% 56% 57% 69%

10. What is the probability that a customer prefers a cheese sandwich or prefers tea?

18% 39% 56% 57% 69%

Short Answer Question:

What is a factorial? Give an example and show how it would be calculated. Then do some research to find an application for factorial in algebra, trigonometry, or calculus. Try to explain in your own words why a factorial appears in that application.