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