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# 11.4 Probability

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• 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)