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Math 1 320 Exam # 3
Name:__________________________________________ ID number:______________ Instructions: Solve the following problems. Show all your work in order to get full credit. Problem 1. A die is weighted in such a way that each of 1, and 3 is twice as likely to come up as each of 2, 4, 5, and 6. Find the probability distribution. What is the probability of rolling less or equal than 4?
Problem 2. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 2; B: the numbers add to 3; C: at least one of the numbers is 1; and D: the numbers do not add to 11. Express the given event in symbols and say how many elements it contains.
- The red die shows 2 and the numbers add to 11.
- The numbers add to 11.
- Either the numbers do not add to 3 or the red die shows a 2.
Problem 4. The following table, which shows the profile, by Math SAT I scores, of admitted students at UCLA for the Fall 2004 semester 200 - 399 400 - 499 500 - 599 600 - 699 700 - 799 Total Admitted 7 212 1124 2882 5309 9534 Not Admitted 687 3512 8689 12230 5150 30268 Total Applicants 694 3724 9813 15112 10459 39802 Compute the theoretical probabilities of the following events:
- An applicant was admitted.
- An admitted applicant had a Math SAT below 500.
- An applicant had a Math SAT below 400 and was admitted.
- An admitted applicant had a Math SAT of 700 or above.
Problem 5. If P ( A ∪ B ) =. 4, P ( A ∩ B ) =. 1, and P ( B )=0.2. Find P ( A ). Problem 6. If 12 businesspeople have a meeting and each pair exchanges business cards, how many business cards, total, get exchanged? Problem 7. A bag contains 5 red marbles, 3 green ones, 2 lavender one, 4 yellows, and 2 orange marbles. a. How many sets of five marbles include one of each color? b. How many sets of five marbles include at least two red ones?
