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# Lesson 4-5

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1. Lesson 4-5 Objectives: To apply ratios to probability.

2. Real World Connection • To analyze a manufacturing situation for quality control, as in Example 3, p. 213.

3. Vocabulary • Probability – how likely it is that something will occur;P(event) • Outcome – the result of a single trial, like one roll of a number cube • Event – any outcome or group of outcomes • Sample space – all the possible outcomes

4. Vocabulary (continued) • Theoretical probability: P(event) / number of possible outcomes **what should happen** • Experimental probability: P(event) = times an event occurs / times done **what actually happens** • Complement of an event -- all outcomes not in the event ( the sum of the probability of an event and its complement is equal to 1)

5. Complement of an Event Example If you have four envelopes labeled A B C D The probability that you will pick envelope A is ¼. The probability of the events complement (not pickingenvelope A) is 1- ¼ = ¾

6. Example 1, page 212 • Suppose you write the names of days of the week on identical pieces of paper. Find the theoretical probability of picking a piece of paper at random that has the name of a day that starts with the letter T.

7. Example 2, page 212 • On a popular television game show, a contestant must choose one of five envelopes. One envelope contains the grand prize, a car. Find the probability of not choosing the car. • In Example 2, what happens to P(not choosing the car) as the number of envelopes increases?

8. Example 3, page 213 • After receiving complaints, a skateboard manufacturer inspected 1000 skateboards at random. The manufacturer found no defects in 992 skateboards What is the probability that a skateboard selected at random had no defects? Write the probability as a percent. • The manufacturer (from example 3 in the book) decides to inspect 2500 skateboards. There are 2450 skateboards that have no defects. Find the probability that a skateboard selected at random has no defects.

9. Example 4, page 213 You can use experimental probability to make a prediction. Predictions are not exact, so round your results. • The manufacturer has 8970 skateboards in its warehouse. If the probability that a skateboard has no defect is 99.2%, predict how many skateboards are likely to have no defect. • A manufacturer inspects 700 light bulbs. She finds that the probability that a light bulb works is 99.6%. There are 35,400 light bulbs in the warehouse. Predict how many light bulbs are likely to work.

10. M & M activity

11. What Colors Come in Your Bag? These are the percentages that was estimated by the M & M company Brown 12% Red 12% Brown 15% Green 15% Blue 23% Orange 23%

12. SUMMARY To find theoretical probability, divide the number of desired outcomes by the number of possible outcomes. **what should happen** To find experimental probability, divide the number of times an event occurs by the number of times the experiment is done.**what actually happens**

13. ASSIGNMENT • #4-5, page 214, 1-22 all, odds 23-45 and odds 51-69