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# Applied Math 40S March 7, 2008

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Probability and counting workshop review problems.

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### Applied Math 40S March 7, 2008

1. 1. A Probability Workshop CHANCE by eisenrah
2. 2. HOMEWORK The probability that Tony will move to Winnipeg is 2/9, and the probability that he will marry Angelina if he moves to Winnipeg is 9/20. The probability that he will marry Angelina if he does not move to Winnipeg is 1/20. Draw a tree diagram to show all outcomes. 1. What is the probability that Tony will move to Winnipeg and marry Angelina? 2. What is the probability that Tony does not move to Winnipeg but does marry Angelina?
3. 3. 3. What is the probability that Tony does not move to Winnipeg and does not marry Angelina?
4. 4. HOMEWORK (a) How many different 4 digit numbers are there in which all the digits are different? (b) If one of these numbers is randomly selected, what is the probability it is odd? (c) What is the probability it is divisable by 5?
5. 5. HOMEWORK An examination consists of thirteen questions. A student must answer only one of the first two questions and only nine of the remaining ones. How many choices of questions does the student have?
6. 6. HOMEWORK Randomly arranged on a bookshelf are 5 thick books, 4 medium-sized books, and 3 thin books. What is the probability that the books of the same size stay together?
7. 7. Randomly arranged on a bookshelf are 5 thick books, 4 medium-sized books, and 3 thin books. How many ways can the 12 books be arranged on a shelf? How many ways can books of the same size stay together? What is the probability that the books of the same size stay together?
8. 8. The Town of Esker The diagram shows a road grid in the town of Esker. The roads are restricted by a river on one side and a lake on the other. Anson lives at point A and his friend Bettina lives at point B. Anson visits Bettina frequently, and likes to take a different route each time. Anson stays on the roads and travels only south and east. How many routes are there from: (a) A to C? (b) C to D? (c) D to B? (d) A to B? (e) A to B if he must go through point P? (f) What is the probability that Anson will go through point P if all routes are randomly chosen?
9. 9. Design an experiment using the random number function of your calculator to determine the probability of passing a six-question multiple choice test if you guess all the answers. Each question has four answers, and one answer is correct in each case. How many simulations would seem reasonable? What is the experimental probability of getting at least 50% on the test?
10. 10. Design an experiment using the random number function of your calculator to determine the probability of passing a six-question multiple choice test if you guess all the answers. Each question has four answers, and one answer is correct in each case. How many simulations would seem reasonable? What is the experimental probability of getting at least 50% on the test?
11. 11. Design an experiment using the random number function of your calculator to determine the probability of passing a six-question multiple choice test if you guess all the answers. Each question has four answers, and one answer is correct in each case. How many simulations would seem reasonable? What is the experimental probability of getting at least 50% on the test?
12. 12. While working on a problem, Chris observed and give the same value but that the value for is larger the the value for . Explain why this outcome occurs.
13. 13. A party of eight boys and eight girls are going for a picnic. Six of the party can ride in one car, and four in another. The rest must walk. (Assume anyone can drive.) (a) In how many ways can the party be distributed for the trip (b) What is the probability that no girl will have to walk? (c) What is the probability that no girl will have to walk if each of the two boys who owns the cars drives his own car?
14. 14. Fred is in a class that has 7 boys and 15 girls. The teacher selects partners for a project by drawing names from a hat. What is the probability that Fred's partner will be a boy?
15. 15. Fred is in a class that has 7 boys and 15 girls. The teacher selects partners for a project by drawing names from a hat. What is the probability that Fred's partner will be a boy?