1. Chapter 2: Understanding Probability 2.6 Theoretical & Experimental Probability

2. Vocab Probability – Tells you how likely an event will occur – Written as P( ) Outcome – Result of a single trial (rolling a die once, etc.) Sample space – List of all the possible outcomes Event – An outcome or a group of outcomes

3. Theoretical Probability Used when the possible outcomes are equally likely to occur P(event) = number of favorable outcomes number of possible outcomes Theoretical: what we *think* will happen

4. probability Can be written as a fraction, a decimal, or a percent Ranges from 0 to 1 – 0 = less likely to occur – 0.5 = equally likely as unlikely – 1 = more likely to occur

5. Example 1 A bowl contains 12 slips of paper, each with a different name of a month. Find the theoretical probability that a slip selected at random from the bowl has a name of a month that starts with the letter J.

6. Example 1a Suppose you write the names of the 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. Complement of an Event Consists of all the outcomes not in the event Example: – I want to roll a 5 on a die – The complement is 1, 2, 3, 4, or 6 The sum of the probabilities of an event and its complement is always 1.

8. Example 2 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.

9. Example 2a What happens to the P(not choosing the car) as the number of envelopes increases?

10. Example 3 Find the odds in favor of a spinner with eight equal sections landing on a number greater than or equal to 6.

11. Example 3a Find the odds against a spinner with eight equal sections landing on a number less than 3.

12. Experimental Probability Probability based on data collected from repeated trials “what actually occurs” instead of “what we want to happen” P(event) = number of times an event occurs number of times the experiment is done

13. Example 4 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?

14. Example 4a The manufacturer inspects 2500 skateboards. There are 2450 skateboards with no defects. Find the probability that a skateboard selected at random has no defects.

15. Example 5 The same manufacturer has 8976 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.

16. Example 5a 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, because she needs to order enough bulbs to cover it.

17. Homework P. 96 1-13, 21-26, 29-38