SECTION 3.1 Basic Concepts of Probability and Counting 139 4 6 8 2 5 3 1 7 H 1 2 3 4 5 6 H3 H2 H1 H4 H5 H6 H7 H8 7 8 T 1 2 3 4 5 6 T3 T2 T1 T4 T5 T6 T7 T8 7 8 Tree Diagram for Coin and Spinner Experiment Probability Applications Using a Tree Diagram A probability experiment consists of tossing a coin and spinning the spinner shown at the left. The spinner is equally likely to land on each number. Use a tree diagram to find the probability of each event. 1. Event A: tossing a tail and spinning an odd number 2. Event B: tossing a head or spinning a number greater than 3 SOLUTION From the tree diagram at the left, you can see that there are 16 outcomes. The outcomes are equally likely to occur, so use the formula for classical probability. 1. There are four outcomes in event A = 5T1, T3, T5, T76. So, P1tossing a tail and spinning an odd number2 = 4 16 = 1 4 = 0.25. 2. There are 13 outcomes in event B = 5H1, H2, H3, H4, H5, H6, H7, H8, T4, T5, T6, T7, T86. So, P1tossing a head or spinning a number greater than 32 = 13 16 ≈ 0.813. TRY IT YOURSELF 10 Find the probability of tossing a tail and spinning a number less than 6. Answer: Page A38 Using the Fundamental Counting Principle Your college identification number consists of eight digits. Each digit can be 0 through 9 and each digit can be repeated. What is the probability of getting your college identification number when randomly generating eight digits? SOLUTION Because each digit can be repeated, there are 10 choices for each of the 8 digits. So, using the Fundamental Counting Principle, there are 10# 10# 10# 10# 10# 10# 10# 10 = 108 = 100,000,000 possible identification numbers. But only one of those numbers corresponds to your college identification number. So, the probability of randomly generating 8 digits and getting your college identification number is 1 100,000,000 , or 0.00000001. TRY IT YOURSELF 11 Your college identification number consists of nine digits. The first two digits of the number will be the last two digits of the year you are scheduled to graduate. The other digits can be any number from 0 through 9, and each digit can be repeated. What is the probability of getting your college identification number when randomly generating the other seven digits? Answer: Page A38 EXAMPLE 10 EXAMPLE 11
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