Lesson 4-5 Objectives: To apply ratios to probability.
Real World Connection • To analyze a manufacturing situation for quality control, as in Example 3, p. 213.
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
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)
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
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.
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?
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.
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.
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%
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**
ASSIGNMENT • #4-5, page 214, 1-22 all, odds 23-45 and odds 51-69