7.1-7.6, 8.1-8.4 Circle the correct classification of the following random variables. Find the values the random variable may have. (4 pts each) 1. Z = the distance a vacationer travels. finite discrete infinite discrete continuous Values of X: x 0 2. U = the number of hours a day a woman works. finite discrete infinite discrete continuous Values of X: 0 x 24 3. Y = the number of tails that occur when a coin is tossed 6 times. finite discrete infinite discrete continuous Values of X: 0, 1, 2, 3, 4, 5, 6 4. X = the number of students draws without replacement to get a blue marble from a box containing 4 red and 5 blue marbles. finite discrete infinite discrete continuous Values of X: 1, 2, 3, 4, 5 The random variable X may only assume the values 2, 3, 4, 5, and 6. Carefully examine the given histogram, and find the following. If necessary, round answers to 3 decimal places. (2 pts each) 9. P(X = 5) = .2 10. P(X >3) = .4 11. Mode of X = 3 0.7 0.6 0.5 12. Median X = 3 13. Var(X) = 1.64 0.4 0.3 0.2 0.1 0 1 2 3 4 5 6 7 8 9 14. Write the non-uniform sample space formed when picking a letter at random from the word MATHEMATICS. (4 pts) {M, A, T, H, E, I, C, S} 15. E and F are mutually exclusive events and P(E) = 0.65 and P(F) = 0.2. Find P(F EC). (4 pts) .35 16. The uniform sample space for an experiment is S = {1, 2, 3, 4, 5}. How many events contain an odd integer? (4 pts) 32 – n(no odd integer) = 32-4 = 28 17. If the probability that Cara passes her math test is 5 , what are the odds that she fails 8 her math test? (4 pts) 3/5 An experiment consists of rolling a fair six-sided die (numbered 1-6) and a fair fivesided die (numbered 1-5). Answer the following four questions about the experiment. (3 pts each) 18. How many events are associated with this experiment? 230 or 1,073,741,824 19. Let E be the event that the six-sided die shows an odd number and let F be the event that the sum of the dice is either 4 or 5. Find P(E F). P(E F) = P(E) + P(F) – P(E F) = 15/30 + 7/30 – 4/30 = 18/30 = 3/5 or .6 20. For the events in problem #19, find P(E | F). P(E | F) = P(E F)/P(F) = (4/30)/(7/30) = 4/7 21. Are the events in problem #19 independent events? Why or why not? No, because P(E F) P(E) P(F) P(E F) = 2/15 and P(E) P(F) = (1/2)(7/30) = 7/60 The letters of the word SUPERCALIFRAGILISTIC are placed on slips of paper and placed into a box. You randomly select 6 pieces of paper from the bag. 22. What is the probability that you select all of the I’s? (4 pts) [C(4,4) C(16,2)]/C(20,6) = 1/323 23. What is the probability that you select at least 5 consonants? (4 pts) [C(12,5)C(8,1) + C(12.6)]/C(20,6) = 121/646 Given the following tree diagram and that G is the event that a student is enrolled in a math class and H is the event that a student is enrolled in a chemistry class, answer the following four questions. (3 pts each) H 0.65 G 0.35 HC 0.4 H 0.6 0.55 GC 0.45 HC 24. What is the probability that a randomly selected student is enrolled in a math class and a chemistry class? .4(.65) = .26 25. What is the probability that a randomly selected math student is enrolled in a chemistry class? .65 26. What is the probability that a randomly selected student is enrolled in a math class? .4 27. What is the probability that a randomly selected chemistry student is not enrolled in a math class? .33/(.26 + .33) = 33/59 28. Draw a tree diagram to represent the following problem. Clearly define your events and indicate the appropriate probabilities on each branch. (12 pts) At the county fair you pay $3.00 to play in the following game. A spinner device is numbered from 1 to 3, and each of the numbers is as likely to come up as any other. You bet $1 on a given number. If the pointer comes to rest on your chosen number, you win $4 (and get the bet back); otherwise, you lose the $1 bet. 29. Find the probability distribution of your net winnings. (6 pts) X P(X) 1 1/3 -4 2/3 30. What are your expected net winnings? (4 pts) E(X) = 1(1/3) – 4(2/3) = 1/3 – 8/3 = -7/3 -2.33, a loss of $2.33 31. If the winnings stay the same, what should be the price for the game to make it a fair game? (4 pts) 1/3(4 – P) + (2/3)(-1 – P) = 0 P = 2/3 The price should be 67 cents to make the game fair.