Quiz 6.3C Here are the counts (in thousands) of earned degrees in the United States in a recent year, classified by level and by the sex of the degree recipient: Bachelor’s Master’s Professional Doctorate Total Female 616 194 30 16 856 Male 529 171 44 26 770 1145 365 74 42 1626

Chapter 6 Review

1. If a peanut M&M is chosen at random, the chances of it being of a particular color are shown in the table below. Color Brown Red Yellow Green Orange Blue Probability .2 .2 .2 .2 .1 The probability of randomly drawing a blue peanut M&M is (a) 0.1 (b) 0.2 (c) 0.3 (d) 1.0 (e) According to this distribution, it’s impossible to draw a blue peanut M&M.

2. Which of the following pairs of events are disjoint (mutually exclusive)? (a) A: the odd numbers; B: the number 3 (b) A: the even numbers; B: the numbers greater than 12 (c) A: the numbers less than 3; B: all negative numbers (d) A: the numbers above 50; B: the numbers less than –50 Reminder

(a) Yes, by the multiplication rule 3. Data show that 14% of the civilian labor force has at least 4 years of college and that 10% of the labor force works as laborers or operators of machines or vehicles. Can you conclude that because (0.14)(0.10) = .014 about 1% of the labor force are college-educated laborers or operators? (a) Yes, by the multiplication rule (b) Yes, by conditional probabilities (c) Yes, by the law of large numbers (d) No, because the events are not independent (e) No, because the events are not mutually exclusive Reminder

4. Which of the following are true? I. The sum of the probabilities in a probability distribution can be any number between 0 and 1. II. The probability of the union of two events is the sum of the probabilities of those events. III. The probability that an event happens is equal to 1 – (the probability that the event does not happen). (a) I and II only (b) I and III only (c) II and III only (d) I, II, and III (e) None of the above gives the complete set of true responses

5. If AB = S (sample space), P(A and Bc) = 0. 15, and P(Ac) = 0 5. If AB = S (sample space), P(A and Bc) = 0.15, and P(Ac) = 0.40, then P(B) = (a) 0.15 (b) 0.45 (c) 0.65 (d) 0.85

A bag contains 4 orange tags numbered 1 – 4 and two black tags numbered 1 – 2. One tag is drawn at random. List the sample space. Calculate the following probabilities. P(orange) 8. P(even number) P(Black and odd) 10. P(orange or odd) 11. P(neither orange nor odd)

A bag contains 4 orange tags numbered 1 – 4 and two black tags numbered 1 – 2. One tag is drawn at random. P(odd|orange) 13. P(orange|even) 14. P(<3|odd)

15. Suppose the probability of eating popcorn is 15. Suppose the probability of eating popcorn is .4 and that the probability of drinking Sprite is .8. Further suppose that the probability of eating popcorn and drinking Sprite is .32. Are these two events independent? How do you know?

Consider this experiment: the letters in the word MISSISSIPPI are printed on square pieces of tagboard (same size squares) with one letter per card. The eleven letter cards are then placed in a top hat, and one letter card is randomly chosen (without looking) from the hat with replacement. List the sample space of all possible outcomes. S = { }

Make a table that shows the set of outcomes (X) and the probability of each outcome: P(X) Outcomes (x) I M P S P(X) 4/11 1/11 2/11

18. Consider the following events: C: a consonant V: a vowel F: the letter chosen falls in the first half of the alphabet (A to M). List the outcomes and give the probability: V = { } P(V) = C = { } P(C) = F = { } P(F) = V or F = { } P(V or F) = complement of C = { } P(Cc) = 19. Are events V and F independent? Explain.

The chart below describes the probabilities of the age in years and the sex of randomly selected students. Age 14-17 18-24 25-34 ≥35 Male .01 .30 .12 .04 Female .01 .30 .13 .09 What is the probability the student is male? What is the conditional probability that the student is male given that the student is between 18 – 24? 22. What is the probability that the student is either male or between 18 – 24?

If four cards are drawn from a standard deck of 52 playing cards and not replaced, find the probability of getting at least one spade. If four dice are rolled, find the probability of getting quads – 1,1,1,1 or 2,2,2,2, etc.

Reminder Disjoint – mutually exclusive (no outcomes in common, never occur simultaneously, one happens then the other. Independent – knowing one outcome doesn’t change the other outcome.

Answers A 2. D 3. D 4. E 5. D 6. O1, O2, O3, O4, B1, B2 7. 4/6 = 2/3 8. 3/6 =1/2 9. 1/6 10. 5/6 11. 1/6 12. 1/2 13. 2/3 14. 2/3 15. Yes .4(.8) = .32 16. M, I, S, P 17. See slide 18. a. I; 4/11 b. M,P, S; 7/11 c. I, M; 5/11 d. I, M; 5/11 e. I; 4/11 19. no; 4/11 ≠ (4/11)(5/11) 20. .47 21. P(M|18-24) = ½ 22. .47 + .30 = .77 23. 1 - P(0 spades) = 1- [(39/52)(38/51)(37/50)(36/49)] = 1-.304 = .696 24. 6/1296 or 1/216