40 minutes exam with 5 to 8 questions.
Math 123 Fall 2017 Dr. Lily Yen Assignment 2 Show all your work Name: Number: Signature: Score: /20 Problem 1: Short answer questions, one mark each. a. If the probability that your DVD player breaks down before the extended warranty expires is 0.067, what is the probability that the player will not break down before the warranty expires? b. In a given year, 1 877 163 males and 1 736 721 females were born in a certain country. If a child is selected randomly from this group, what is the probability that the child is female? c. The residents of a small town and the surrounding area are divided over the proposed construction of a dog park in town, as shown in the table. A reporter randomly selects a person to interview from a group of residents. If the person selected supports the dog park, what is the probability that the person lives in town? Support dog park Oppose dog park Live in town 7252 6316 Live in surrounding area 518 461 d. When you roll a pair of dice, what is the probability of getting a sum of at least 10? e. When you draw a single card from a deck of 52 cards, what is the probability of getting either a spade or a queen? f. Assume that A and B are events. If P (A∪B) = 0.7, P (A) = 0.3, and P (A∩B) = 0.15, find P (B). Score: /6 Problem 2: Write the event as a set of outcomes: Red appears at least once when we spin two times a spinner which contains a third of red, a third of blue, and a third of yellow. Score: /2 Problem 3: A game has two four-sided dice having the numbers 7, 6, 3, and 8 on their faces. Outcomes in the sample space are pairs such as (7, 3), and (6, 6). a. Draw the sample space. b. Express the event “the total showing is an odd number” as a set. c. Find the probability that the total showing is more than 10. Score: /4 Problem 4: The table shows the age distribution of those who earned less than mini- mum wage in a recent year. If a worker is randomly selected from those surveyed, find the probability that the person is older than 34. Age Working below minimum wage 16–19 337 000 20–24 417 000 25–34 331 000 35–44 168 000 45–54 113 000 55–64 80 000 65 and older 37 000 Score: /2 Problem 5: The table relates the amount of time consumers engage in online shopping per month with their annual income. Find the probability that a randomly selected consumer either spends 0–2 hours per month shopping online or has an annual income below $40 000. Annual income 10 h or more 3 h–9 h 0 h–2 h Total Above $60 000 188 179 129 496 $40 000–$60 000 147 216 160 523 Below $40 000 129 188 253 570 Total 464 583 542 1589 Score: /3 Problem 6: A candy jar contains 50 green jelly beans, 35 pink jelly beans, and 15 white jelly beans. Two jelly beans are randomly selected without replacement. Let G be the event you select a green jelly bean first, and let N be the event the second jelly bean is not green. Find P (G | N). Score: /3 Page 2 Math 123 Example Randomly select two bills from the pot (without replace- ment). $0 $1 $2 $5 Second Bill $0 $1 $2 $5 $0 – (0,1) (0,2) (5,0) First $1 (1,0) – (1,2) (1,5) Bill $2 (2,0) (2,1) – (2,5) $5 (5,0) (5,1) (5,2) – 1. What is the chance of getting at least $5? 2. What is the chance of getting no more than $3? 69 Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Odds Definition The odds against event E Practice exercises in Section 13.1: all odds from 1–31. 70 Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen 13.2 Complements and Unions of Events Venn Diagrams: 1. One event E in a sample space S. 2. A and B: the event that both A and B occur. 3. A or B: the event that A or B or both occur. Theorem 1. General case: 2. 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