Section Theoretical and Experimental Probability...Wks 3


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1 Name: Class: Date: Section Theoretical and Experimental Probability...Wks 3. Eight balls numbered from to 8 are placed in a basket. One ball is selected at random. Find the probability that it is not number 2. 3 a c. 8 d A number cube is rolled 20 times. The number six comes up 22 times. a. What is the theoretical probability of rolling a six? What is the experimental probability of rolling a six? 3. You are using the spinner below to play a board game. During your turn you spin the spinner. Find the probability of going back. 4. The table shows the drink preferences of 50 shoppers at a mall. What is the probability that shopper, selected at random from the 50 surveyed, preferred either Drink A or Drink D? 7 a. 2, c d A sixsided number cube is rolled 350 times and the results are recorded as follows: 58 ones, 63 twos, 52 threes, 6 fours, 60 fives, and 56 sixes. What is the experimental probability of not rolling a five? Round to the nearest whole percent if necessary. a. 83% 93% c. 7% d. 7% 6. You work at a Tshirt printing business. Of 300 Tshirts shipped, 55 are printed improperly. What is the experimental probability that a Tshirt is printed correctly?
2 Name: 7. A sixsided number cube numbered through 6 is rolled 270 times. The number 3 comes up 44 times. a. What is the theoretical probability of rolling a 3? What is the experimental probability of rolling a 3? a. not enough information a. 6 c. a d. a In your last 25 basketball games, you attempted 50 free throws and made 50. What is the experimental probability of you making a free throw in your next game? 9. At the Rockville Middle School carnival, 4 of the first 60 people who played the ring toss game won the first prize, 8 won the second prize, and 2 won the third prize. What is the experimental probability of not winning the first, second, or third prize? a c d The chart shows the results of spinning the spinner 44 times. 0. A bag holds 2 red marbles and 3 green marbles. Gwen takes a marble out of the bag, records the color, then replaces the marble in the bag. She does this 20 times and records her results below. a. Are the outcomes for the experiment equally likely? Find the experimental probability that a red marble will be chosen from the bag. Write your result as a decimal. Round to the nearest hundredth when necessary. a. a. Yes 0.4 a. Yes 0.6 c. a. No 0.4 d. a. No 0.6 Number Number 2 Number 3 Number a. Find the experimental probability of the spinner landing on the number 2. Write your answer as a fraction and as a decimal rounded to the nearest hundredth. Find the experimental probability of the spinner not landing on the number 4. Write your answer as a fraction and as a decimal rounded to the nearest hundredth. 2
3 Name: 2. Students in Mr. Zang's fifth period math class took turns tossing a fair coin. They were paired into two groups and their results are recorded in the table below. 5. The table shows the soft drink preferences of 50 shoppers at the mall. What is the probability that shopper, selected at random from the 50 surveyed, preferred either Drink A or Drink B? DRINK SURVEY Drink Number of Shoppers a. How many heads were tossed in group A? Find the experimental probability of tails coming up for each group of students. Write your answer as a decimal. 3. What is the experimental probability that the spinner stops on G? Write your answer as a fraction. Outcome Total B 26 G 24 Y 3 R 33 A 5 B 0 C 7 D 7 E 6. Two sixsided number cubes each have sides numbered through 6. a. Describe an outcome that is impossible. Describe an outcome that is certain. 7. You are one of 20 people entering a contest. What is the theoretical probability that your name will be drawn first? a. 9 0 c. 20 d A 6sided number cube is rolled 35 times. On 27 of the rolls, the outcome was a five. What is the experimental probability of rolling a five? Write your answer as as a fraction and as a decimal. 3
4 Name: 8. A brown paper bag contained 0 cubes, colored either red or yellow. Each of 25 students selected a cube from the bag without looking, recorded the color in the chart below, and replaced the cube. Based on the results shown in the chart, which is the best prediction of the number of red and yellow cubes in the bag? a. 4 red cubes and 6 yellow cubes 3 red cubes and 7 yellow cubes c. 7 red cubes and 3 yellow cubes d. 6 red cubes and 4 yellow cubes Writing: 22. The manager of a hardware store took a random sample of 4.5 pounds of nails from a delivery of 350 pounds of nails. The manager found that 0.3 pounds of nails in the sample were defective. They were either bent, the heads were damaged, or they had been clipped too short during manufacture. How many pounds of defective nails should the manager expect the 350pound delivery to contain? Round your answer to the nearest tenth of a pound. 23. Every day, a random sample of 275 computer memory chips produced by a factory is tested to see if the chips meet their minimum speed ratings for certain operations. If 5 of the chips failed the test on a day when 22,000 chips were made, which is the best estimate of the number of memory chips made that day that are likely to meet the minimum speed ratings for those operations? Round the answer to the nearest ten. a. 2, c. 370 d. 23,0 9. Explain what theoretical probability is and how to find it. Be sure to include the formula. 20. Explain what experimental probability is and how to find it. Be sure to include the formula. 2. The chart shows the results of spinning the spinner 4 times. Number Number 2 Number 3 Number a. Find the experimental probability of the spinner landing on the number 2. Write your answer as a fraction and as a percent rounded to the nearest tenth. Find the experimental probability of the spinner not landing on the number 4. Write your answer as a fraction and as a percent rounded to the nearest tenth. 4
5 Section Theoretical and Experimental Probability...Wks 3 Answer Section. C 2. a C 5. A 6. 95% 7. C D 0. C. a ; ; a. 208 heads Group A: 0.48; Group B: or , Answers will vary. a. Possible answer: a sum of on the two number cubes. Possible answer: a number less than 4 7. C 8. A 9. Sample answer: Theoretical probability is applied when all the possible outcomes of an experiment are equally likely to occur. To find the theoretical probability of an event E under these circumstances, use the ratio number of favorable outcomes P( E) = number of possible outcomes. 20. Sample answer: Experimental probability is based on the observed results of an experiment. To find the experimental probability of an event E under these circumstances, use the ratio number of times event E happens P( E) = number of times the experimentis done. 2. a. 5 4 ; 36.6% 36 4 ; 87.8% pounds
6 23. A 2
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