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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

Section 6.2.3Probability Models

AP Statistics

toddfadoir.com/apstats

definition of independence
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
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
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
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
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 independent1
Are these events independent?
  • A={person is college graduate}
  • B={person is older than 25}
  • C={person is a bank president}

AP Statistics, Section 6.2, Part 3

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

AP Statistics, Section 6.2, Part 3