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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up 1. Two coins are tossed. What is the probability of getting two heads? 2. Give the probability that the roll of a number cube will show 1 or 4.

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. Warm Up 1. Two coins are tossed. What is the probability of getting two heads? 2. Give the probability that the roll of a number cube will show 1 or 4. 3. Give the expected number of rolls that will result in a 2 if a number cube is rolled 42 times. 1 4 1 3 7

  3. Problem of the Day The name of a U.S. state is spelled out with letter tiles. Then the tiles are placed in a bag, and one is picked at random. What state was spelled out if the probability of picking the letter O is 1 2 ? 3 8 1 3 ? ? Ohio; Colorado; Oregon

  4. Sunshine State Standards MA.7.P.7.2 Determine, compare, and make predictions based on theoretical…probability… AlsoMA.7.P.7.1

  5. Vocabulary theoretical probability equally likely fair

  6. Theoretical probability is used to find the probability of an event when all the outcomes are equally likely. Equally likelyoutcomes have the same probability. If each possible outcome of an experiment is equally likely, then the experiment is said to be fair. Experiments involving number cubes and coins are usually assumed to be fair.

  7. 9 20 = 9 20 Additional Example 1A: Finding Theoretical Probability Andy has 20 marbles in a bag. Of these, 9 are clear and 11 are blue. Find the probability of drawing a clear marble from the bag.Write your answer as a fraction, as a decimal, and as a percent. number of ways the event can occur total number of equally likely outcomes P = number of clear marbles total number of marbles P(clear) = Write the ratio. Substitute. Write as a decimal and write as a percent. = 0.45 = 45% The theoretical probability of drawing a clear marble is , 0.45, or 45%.

  8. 11 20 = Additional Example 1B: Finding Theoretical Probability Find the probability of drawing a blue marble from the bag. number of ways the event can occur total number of equally likely outcomes P = number of blue marbles total number of marbles P(blue) = Write the ratio. Substitute. Write as a decimal and write as a percent. = 0.55 = 55% The theoretical probability of drawing a blue marble is , 0.55, or 55%. 11 20

  9. Check It Out: Example 1A Dalek is drawing numbered balls from a bin. There are 20 balls numbered 1 through 20. Find the probability of each event. Write your answer as fraction, a decimal, and a percent. drawing a ball numbered 4 or lower number of ways the event can occur total number of equally likely outcomes P = 4 20 = 1 5 = = 0.2= 20% P (4 or lower)

  10. number of ways the event can occur total number of equally likely outcomes P = Check It Out: Example 1B Dalek is drawing numbered balls from a bin. There are 20 balls numbered 1 through 20. Find the probability of each event. Write your answer as fraction, a decimal, and a percent. drawing an odd-numbered ball The odd-numbered balls are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, for a total of 10 balls. 1 2 10 20 P (odd numbered) = = 0.5 = 50% =

  11. number of boys on the team number of members on the team P(boy) = Additional Example 2A: School Application There are 13 boys and 10 girls on the track team. The name of each of the team members is written on an index card. A card is drawn at random to choose a student to run a sprint and the card is replaced in the stack. Find the theoretical probability of drawing a boy’s name. 13 23 P(boy)= Substitute.

  12. Remember! The sum of the probabilities of an event and its complement is 1.

  13. 13 23 Substitute for P(boy). 13 23 Subtract from both sides Simplify. Additional Example 2B: School Application There are 13 boys and 10 girls on the track team. The name of each of the team members is written on an index card. A card is drawn at random to choose a student to run a sprint and the card is replaced in the stack. Find the theoretical probability of drawing a girl’s name. P(boy) + P(girl) = 1 13 23 + P(girl) = 1 13 23 13 23 - = - 10 23 P(girl) =

  14. number of boy’s names total number of students P = Check It Out: Example 2A There are 15 boys and 12 girls in Sharon’s math class. Each of their names is written on a slip of paper and put in a hat. Find the theoretical probability of drawing a boy’s name. 5 g 15 27 P(boy) = =

  15. Check It Out: Example 2B There are 15 boys and 12 girls in Sharon’s math class. Each of their names is written on a slip of paper and put in a hat. Find the theoretical probability of drawing a girl’s name. P(boy) + P(girl) = 1 5 9 + P(girl) = 1 4 9 P(girl) =

  16. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  17. Lesson Quiz Find the probabilities. Write your answer as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent. You have 11 cards, each with one of the letters from the word mathematics. 1. Find the probability of drawing an m from the pile of shuffled cards. 2. Find the probability of drawing a vowel. 3. Find the probability of drawing a consonant. 2 11 , 0.18, 18% 4 11 , 0.36, 36% , 0.64, 64% 7 11

  18. Lesson Quiz for Student Response Systems 1. A number cube is rolled. Identify the probability of getting a number less than 4 as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent. A. B. C. D.

  19. Lesson Quiz for Student Response Systems 2. There are 40 balls in a bag. Of these 8 are white, 7 are blue, 12 are green, and 13 are yellow. Identify the probability of drawing a white ball as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent. A. B. C. D.

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