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# 11.4 Probability

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### 11.4 Probability

1. 1. 11.4 Fundamentals of Probability<br />
2. 2. Some important questions<br />What is probability?<br />Why study probability?<br />What is the probability of winning the Maryland lottery?<br />What is the probability of being struck by a lightning?<br />What is the probability of getting an A in the class?<br />
3. 3. Computing Theoretical Probability<br />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<br /> P(E) = number of outcomes in event E = n(E)<br /> total # of possible outcomes n(S)<br />
4. 4. Example 1<br />A die is rolled once. Find the probability of getting:<br />a. 5<br /> b. an even number<br /> c. a number greater than 2<br /> d. a number less than 6<br /> e. a number greater than 4<br />
5. 5. Example 2<br />You are dealt a standard 52-card deck. Find the probability of being dealt<br />A. A king<br />B. A red card<br />C. A five<br />D. A picture card<br />E. A red queen<br />F. A club<br />
6. 6. Probabilities in Genetics<br />Blood type problem: What is the chance of having a blood type AB if your parents have types AO and BB.<br />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? <br />
7. 7. Empirical Probability<br />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.<br />P (E) = observed number of times E occurs<br /> total number of observed occurences<br />
8. 8. Example<br />Marital Status of the US Population , Ages 18 or older in millions<br />Source: US Census Bureau<br />
9. 9. Questions:<br />What is the probability of randomly selecting a female?<br />What is the probability of randomly selecting a divorced person?<br />What is the probability of randomly selecting a married male?<br />
10. 10. Assignments<br />Classwork: Checkpoints 1-4 p. 580-584<br />And do #s 2-30 (evens)<br />HW: p. 585-586, #s 1-39 (odd); 49-63 (odd)<br />