Event 2 flipping a coin has 2 possible outcomes 6 2

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Event 2: Flipping a coin has 2 possible outcomes. 6 × 2 = 12 Fundamental Counting Principle There are 12 possible outcomes. EXAMPLE Finding the Total Number of Possible Outcomes 3 How many different outfits can you make from the T-shirts, jeans, and shoes in the closet? Use the Fundamental Counting Principle. Identify the number of possible outcomes for each event. Event 1: Choosing a T-shirt has 7 possible outcomes. Event 2: Choosing jeans has 4 possible outcomes. Event 3: Choosing shoes has 3 possible outcomes. 7 × 4 × 3 = 84 Fundamental Counting Principle So, you can make 84 different outfits. 2. Find the total number of possible outcomes of spinning the spinner and choosing a number from 1 to 5. 3. How many different outfits can you make from 4 T-shirts, 5 pairs of jeans, and 5 pairs of shoes? Exercises 8 –11
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424 Chapter 10 Probability and Statistics A compound event consists of two or more events. As with a single event, the probability of a compound event is the ratio of the number of favorable outcomes to the number of possible outcomes. EXAMPLE Finding the Probability of a Compound Event 4 EXAMPLE Finding the Probability of a Compound Event 5 In Example 2, what is the probability of rolling a number greater than 4 and flipping tails? There are two favorable outcomes in the sample space for rolling a number greater than 4 and flipping tails: 5T and 6T. P (event) = number of favorable outcomes ——— number of possible outcomes P (greater than 4 and tails) = 2 12 Substitute. = 1 6 Simplify. The probability is 1 6 , or 16 2 3 %. You flip three nickels. What is the probability of flipping two heads and one tails? Use a tree diagram to find the sample space. Let H = heads and T = tails. There are three favorable outcomes in the sample space for flipping two heads and one tails: HHT, HTH, and THH. P (event) = number of favorable outcomes ——— number of possible outcomes P (2 heads and 1 tails) = 3 8 Substitute. The probability is 3 8 , or 37.5%. 4. In Example 2, what is the probability of rolling at most 4 and flipping heads? 5. In Example 5, what is the probability of flipping at least two tails? 6. You roll two number cubes. What is the probability of rolling double threes? 7. In Example 1, what is the probability of choosing a stuffed crust Hawaiian pizza? Exercises 15–24 H H H H H T T H H T H H H T T T H H T T H T T T H H H T T H T T H H T T T T T T H
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Section 10.4 Compound Events 425 Exercises 10.4 Help with Homework 9 +(-6)=3 3 +(-3)= 4 +(-9)= 9 +(-1)= 5. COMBINATIONS The lock is numbered from 0 to 49. Each combination uses three numbers in a right, left, right pattern. Find the total number of possible combinations for the lock. Use a tree diagram to find the sample space and the total number of possible outcomes. 6. 7. Birthday Party Event Miniature golf, Laser tag, Roller skating Time 1:00 p.m. – 3:00 p.m. , 6:00 p.m. – 8:00 p.m.
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