4 the theoretical probability of spinning an odd

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4. The theoretical probability of spinning an odd number on a spinner is 0.6. The spinner has 10 sections. How many sections have odd numbers? 5. The prize wheel in Example 4 was spun 540 times at a baseball game. About how many bobbleheads would you expect were won? EXAMPLE Comparing Experimental and Theoretical Probability 5 The bar graph shows the results of rolling a number cube 300 times. a. What is the experimental probability of rolling an odd number? The bar graph shows 48 ones, 50 threes, and 49 fives. So, an odd number was rolled 48 + 50 + 49 = 147 times in a total of 300 rolls. P (event) = number of times the event occurs ——— total number of trials P (odd) = 147 300 = 49 100 , or 49% b. How does the experimental probability compare with the theoretical probability of rolling an odd number? In Section 10.2, Example 2, you found that the theoretical probability of rolling an odd number is 50%. The experimental probability, 49%, is close to the theoretical probability. c. Compare the experimental probability in part (a) to the experimental probability in Example 1. As the number of trials increased from 50 to 300, the experimental probability decreased from 58% to 49%. So, it became closer to the theoretical probability of 50%. 6. Use the bar graph in Example 5 to find the experimental probability of rolling a number greater than 1. Compare the experimental probability to the theoretical probability of rolling a number greater than 1. Times rolled Rolling a Number Cube 36 48 60 0 12 24 72 1 2 3 4 5 6 Number rolled 48 49 50 48 52 53 An odd number was rolled 147 times. There was a total of 300 rolls. Exercises 25–27 a a b be er
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Section 10.3 Experimental and Theoretical Probability 417 Use the bar graph to find the relative frequency of the event. 6. Spinning a 6 7. Spinning an even number Use the bar graph to find the experimental probability of the event. 8. Spinning a number less than 3 9. Not spinning a 1 10. Spinning a 1 or a 3 11. Spinning a 7 12. EGGS You check 20 cartons of eggs. Three of the cartons have at least one cracked egg. What is the experimental probability that a carton of eggs has at least one cracked egg? 13. BOARD GAME There are 105 lettered tiles in a board game. You choose the tiles shown. How many of the 105 tiles would you expect to be vowels? 14. CARDS You have a package of 20 assorted thank-you cards. You pick the four cards shown. How many of the 20 cards would you expect to have flowers on them? Exercises 10.3 Help with Homework 1. VOCABULARY Describe how to find the experimental probability of an event. 2. REASONING You flip a coin 10 times and find the experimental probability of flipping tails to be 0.7. Does this seem reasonable? Explain. 3. VOCABULARY An event has a theoretical probability of 0.5. What does this mean? 4. OPEN-ENDED Describe an event that has a theoretical probability of 1 4 .
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