CONDITIONAL PROBABILITY AND TWO-WAY TABLES

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1 CONDITIONAL PROBABILITY AND TWO-WAY TABLES The probability of one event occurring, knowing that another event has already occurred is called a conditional probability. Two-way tables are useful for representing conditional probability situations. For additional information see the Math Notes boxes in Lessons and Example # #2 For the spinners at right, assume that the smaller sections of spinner # are half the size of the larger section and for spinner #2 assume that the smaller sections are one-third the size of the larger section. R G B R G B Y a. Draw a diagram for spinning each spinner once. What is the probability of getting the same color twice? If you know you got the same color twice, what is the probability it was red? The diagram for part (a) is shown at right. Note that the boxes do not need to be to scale. The circled boxes indicate getting the same color, so the total probability for part (b) is: = 2 =. For part (c), both red (RR) is 8 out of the from part (b). Therefore, the probability that both spins were red knowing that you got the same color twice is 8 = 8 = 2. Parent Guide with Extra Practice 205 CPM Educational Program. All rights reserved. 85

2 Chapter 7 Example 2 A soda company conducted a taste test for three different kinds of soda that it makes. It surveyed 200 people in each age group about their favorite flavor and the results are shown in the table below. Age Soda A Soda B Soda C Under to to and over 9 0 a. What is the probability that a participant chose Soda C or was under 20 years old? What is the probability that Soda A was chosen? If Soda A was chosen, what is the probability that the participant was 0 years old or older? For part (a), using the Addition Rule: P(C or < 20) = P(C) + P(< 20) P(C and < 20) = = = , or about 38%. For part (b), add the number of participants selecting Soda A: = = 0.075, or about %. For part (c), take only the participants over 0 who selected Soda A out of all those selecting Soda A: , or about 3%. Problems. Two six-sided dice are thrown. a. How many ways are there to get 7 points? What is the probability of getting 7 points? If you got 7 points, what is the probability that the result on one of the dice was a 5? 2. Elizabeth and Scott are playing a game at the state fair that uses two spinners that are shown in the diagrams at right. The player spins both wheels and if the colors match the player wins a prize. a. Make a probability diagram for this situation. What is the probability of winning a prize? If you won a prize, what is the probability that the matching colors were red? Spinner # B: R: Spinner #2 R G B Y CPM Educational Program. All rights reserved. Core Connections Integrated II

3 3. An airline wants to determine if passengers not checking luggage is related to people being on business trips. Data for 000 random passengers at an airport was collected and summarized in the table below. Checked Baggage No Checked Baggage Traveling for business Not traveling for business 2 29 a. What is the probability that a passenger did not check baggage? If a passenger is traveling for business, what is the probability that the passenger did not check baggage?. In Canada, 92% of the households have televisions. 72% of households have televisions and Internet access. What is the probability that a house has Internet given that it has a television? 5. There is a 25% chance that Claire will have to work tonight and cannot study for the big math test. If Claire studies, then she has an 80% chance of earning a good grade. If she does not study, she only has a 30% chance of earning a good grade. a. Draw a diagram to represent this situation. Calculate the probability of Claire earning a good grade on the math test. If Claire earned a good grade, what is the probability that she studied?. A bag contains blue marbles and 2 yellow marbles. Two marbles are randomly chosen (the first marble is NOT replaced before drawing the second one). a. What is the probability that both marbles are blue? What is the probability that both marbles are yellow? What is the probability of one blue and then one yellow? d. If you are told that both selected marbles are the same color, what is the probability that both are blue? Parent Guide with Extra Practice 205 CPM Educational Program. All rights reserved. 87

4 Chapter 7 7. At Cal s Computer Warehouse, Cal wants to know the probability that a customer who comes into his store will buy a computer or a printer. He collected the following data during a recent week: 233 customers entered the store, 2 purchased computers, purchased printers, and 93 made no purchase. a. Draw a Venn diagram to represent the situation. Based on this data, what is the probability that the next customer who comes into the store will buy a computer or a printer? Cal has promised a raise for his salespeople if they can increase the probability that the customers who buy computers also buy printers. For the given data, what is the probability that if a customer bought a computer, he or she also bought a printer? 8. A survey of 200 recent high school graduates found that 70 had driver licenses and 08 had jobs. Twenty-one graduates said that they had neither a driver license nor a jo a. Draw a two-way table to represent the situation. If one of these 200 graduates is randomly selected, what is the probability that he or she has a job and no license? If the randomly selected graduate is known to have a job, what is the probability that he or she has a license? 9. At McDougal s Giant Hotdogs 5% of the workers are under 8 years old. The most desirable shift is to 8 p.m. and 80% of the workers under 8 years old have that shift. 30% of the workers who are 8 years or older have the to 8 p.m. shift. a. Represent these probabilities in a two-way table. What is the probability that a randomly selected worker is 8 or over and does not work the to 8 p.m. shift? What is the probability that a randomly selected worker from the to 8 p.m. shift is under 8 years old? CPM Educational Program. All rights reserved. Core Connections Integrated II

5 Answers. a. ways 3 = = 3 2. a. See diagram at right. + 2 = = a = % 92% 78% 5. a. See diagram at right = 0.75 = 7.5% %. a. 3 5 = = = 5 d. 2 5 ( ) = 7 Work (not study) (0.25) No work (study) (0.75) Good grade (0.3) Bad grade (0.7) Good grade (0.8) Bad grade (0.2) 7. a. computer printer a. See diagram at right Job No job License No li a. See diagram at right p.m. Other (0.5)(0.80) = (0.85)(0.30) = Parent Guide with Extra Practice 205 CPM Educational Program. All rights reserved. 89 < 8 8

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