Section 6.2.3 Probability Models

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# Section 6.2.3 Probability Models - PowerPoint PPT Presentation

Section 6.2.3 Probability Models. AP Statistics toddfadoir.com/apstats. Definition of Independence. Two events A and B are independent if knowing that one occurs does not change the probability of that the other occurs. If A and B are independent,

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## Section 6.2.3 Probability Models

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### Section 6.2.3Probability Models

AP Statistics

Definition of Independence

Two events A and B are independent if knowing that one occurs does not change the probability of that the other occurs.

If A and B are independent,

This is the multiplication rule for independent events

AP Statistics, Section 6.2, Part 3

Example of Independent Events
• First coin flip, second coin flip
• Rolling of two dice
• Choosing two cards with replacement

AP Statistics, Section 6.2, Part 3

Example of Not Independent Events
• Choosing two cards without replacement
• Scoring above 600 on verbal SAT, scoring 600 on math SAT

AP Statistics, Section 6.2, Part 3

Independent and complements
• If A and B are independent, then so are…
• Ac and Bc
• A and Bc
• Ac and B

AP Statistics, Section 6.2, Part 3

Are these events independent?
• A={person is left-handed}
• B={person is an only child}
• C={person is blue eyed}

AP Statistics, Section 6.2, Part 3

Are these events independent?
• B={person is older than 25}
• C={person is a bank president}

AP Statistics, Section 6.2, Part 3

Traffic light example
• Suppose the timing of the lights on morning commute are independent.
• The probability of being stopped at any light is .6.
• P(getting through all 6 lights)
• .46=.004096
• P(getting stopped at all the lights)
• .66=.046656

AP Statistics, Section 6.2, Part 3

Assignment
• Exercises: 6.27-6.33 all, 6.35-6.45 odd

AP Statistics, Section 6.2, Part 3