1. PIB Geometry Probability 1 - Experimental and Theoretical Probability

2. Warm Up New seats

3. What’s coming up? For the next two weeks, we will be working on a probability unit. Since our current texts do not have any probability, we will be working out of an online textbook, which is available on my website.my website You can leave your textbook at home! https://www.fairviewhs.org/staff/jack- cawelti/classes/pib-geometry/calendar https://www.fairviewhs.org/staff/jack- cawelti/classes/pib-geometry/calendar

4. Probability Probability Theory is the study of the chance (likelihood) of events occurring. Origins: http://en.wikipedia.org/wiki/Problem_of_points http://en.wikipedia.org/wiki/Problem_of_points Two types of probability: Theoretical vs. Experimental

5. The probability of an event is always between 0 and 1; expressible as fraction, decimal, or percent. 0 means: 1 means: Ex) What is P(roll a 3 on a die labeled 1 to 6)? Ex) P(roll a 7 on a die labeled 1 to 6)?

6. Experimental Probability - Vocab Number of Trials Outcomes Frequency of an outcome Relative frequency of an outcome

7. Experimental Probability

8. Example Ex) A die is rolled 8 times with the following results: {1,5,3,6,1,2,4,5} What is the experimental probability of rolling a 5? Rolling a 6? Rolling an even number? Rolling at least a 4?

9. You try! The graph shows the frequency of grades on Ms. Pfenning’s final exam out of 100 total students. What is the probability that a randomly chosen student received a score in the 60s? Received a passing grade? What is the probability that a student received a score in the 60s, given that he/she passed?

10. The following table shows how much a group of college students study per week. 1.How many students study more than 10 hours? 2.P(randomly chosen student studies 40 hrs. or less)?

12. Theoretical Probability

13. Example A bag contains 3 apples, 8 pears, and 14 oranges. What is the probability that a randomly selected fruit is a pear? What is the probability that it is not a pear? What do you notice about these two numbers?

14. Complementary Events Two events are complementary if they are the only two possible outcomes Ex) Complementary events always sum to ______.

15. Example Suppose you roll two dice at the same time. Determine the probability that you do not roll doubles.

16. A coin is tossed 3 times… List all the possible outcomes What is the probability that all 3 tosses are the same?

17. Homework 1 14A: #1-4 all 14C: #1, 2 14E: #1-8 all