# 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

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