Section 6.2.3Probability Models

AP Statistics

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AP Statistics, Section 6.2, Part 3 2

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

( and ) ( ) ( )P A B P A P B

AP Statistics, Section 6.2, Part 3 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 4

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 5

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 6

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 7

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 8

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 9

Assignment

Exercises: 6.27-6.33 all, 6.35-6.45 odd