This document discusses fundamentals of probability, including theoretical and empirical probability. It provides examples of calculating probabilities of events using formulas that take the number of outcomes of an event over the total number of possible outcomes. Examples include probabilities of rolling certain numbers on a die, being dealt certain cards, blood types based on parent genetics, and marital status based on US census data. Assignments are provided for classwork and homework problems.

1. 11.4 Fundamentals of Probability

2. Some important questions What is probability? Why study probability? What is the probability of winning the Maryland lottery? What is the probability of being struck by a lightning? What is the probability of getting an A in the class?

3. Computing Theoretical Probability If an event E has n(E) equally-likely outcomes and its sample space S has n(s) equally-likely outcomes, the theoretical probability of event E, denoted by P(E) is P(E) = number of outcomes in event E = n(E) total # of possible outcomes n(S)

4. Example 1 A die is rolled once. Find the probability of getting: a. 5 b. an even number c. a number greater than 2 d. a number less than 6 e. a number greater than 4

5. Example 2 You are dealt a standard 52-card deck. Find the probability of being dealt A. A king B. A red card C. A five D. A picture card E. A red queen F. A club

6. Probabilities in Genetics Blood type problem: What is the chance of having a blood type AB if your parents have types AO and BB. Dimples: Facial dimples are examples of dominant genes which means that if a person has genotype DD or Dd, he or she will have a dimple. A person with no dimple has a genotype of dd. What is the chance of producing an offspring with a dimple if one parent has a dimple and the other has none?

7. Empirical Probability Theoretical probability is based on a set of equally-likely outcomes and the number of elements in a set. By contrast, empirical probability applies to situations in which we observe the frequency of occurrence of an event. P (E) = observed number of times E occurs total number of observed occurences

8. Example Marital Status of the US Population , Ages 18 or older in millions Source: US Census Bureau

9. Questions: What is the probability of randomly selecting a female? What is the probability of randomly selecting a divorced person? What is the probability of randomly selecting a married male?

10. Assignments Classwork: Checkpoints 1-4 p. 580-584 And do #s 2-30 (evens) HW: p. 585-586, #s 1-39 (odd); 49-63 (odd)