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Chapters 14 and 15

Chapters 14 and 15. All In One Day!. Finding Probability Summary. Equally likely outcomes Determine the fraction They tell us Using rules to calculate Personal probabilities Experimental probabilities. What is Probability?. A number.

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Chapters 14 and 15

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  1. Chapters 14 and 15 All In One Day!

  2. Finding Probability Summary Equally likely outcomes Determine the fraction They tell us Using rules to calculate Personal probabilities Experimental probabilities

  3. What is Probability? A number. Specifically, it represents the long-term likelihood of an event occuring. It is a model for what could happen, not what will happen. It is often expressed as a percentage when talking to people, but when doing calculations it is usually left as a fraction or a decimal.

  4. Definitions • Trial – This is what we call one instance of the random phenomenon. • Outcome – This is the end result of a trial. • Event – This is an outcome or collection of outcomes that we are interested in. • Compliment – The compliment of an event is the set of all outcomes that are not part of the event.

  5. Definitions • Disjoint (Mutually Exclusive) – These are two or more events that cannot happen at the same time. • Dependent – Two events are dependent if knowing that one happened changes the probability of the other. • Independent – Two events are independent if knowing one variable turned out does not affect the other.

  6. Probability Rules • Rule: 0 ≤ P(x) ≤ 1 for each outcome or event. • Rule: The sum of all possible outcomes must equal 1. • This does not have to mean that the sum of all events equals 1. It is specifically outcomes. • Rule: P(Ac) = 1 – P(A)

  7. Probability Rules • Rule: When events are disjoint, we can add their probabilities to calculate the probability of the union of those events. • P(A  B) = P(A) + P(B) (if A and B are disjoint) • Rule: When events are independent, we can multiply their probabilities to calculate the probability of the intersection of those events. • P(A  B) = P(A)P(B) (if A and B are independent)

  8. Probability Rules • General Addition Rule: • P(A  B)= P(A) + P(B) – P(A  B) • P(A  B)= P(A) + P(B) – P(A B) • General Multiplication Rule: • P(A  B) = P(A)  P(B|A)

  9. Probability Assignments • To determine if a probability assignment is legitimate we need to verify two things. • We need to verify that each outcome has a probability between 0 and 1, inclusive. • We also need to verify that all of the outcomes add to a total probability of 1.

  10. Also… • If you have questions about contingency tables, ask now. • If you have questions about Venn diagrams, ask now. • If you have questions about probability trees, ask now. • “At least” is our key to use compliments.

  11. Current Homework • Chapter 16: 15, 25, 32 • Chapter 17: 13, 15, 17, 25 • Presentations are on Feb 17th unless you make other arrangements.

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