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# Section 4.4

### Multiplication Rule

Term | Definition |
---|---|

Notation | P(A & B) = P(event A occurs in a 1st trial & event B occurs in a 2nd trial) |

Conditional Probability | The probability for the 2nd event B should take into account the fact that the 1st event A has already occurred. P(B|A) represents the probability of event B occurring after it is assumed that event A has already occurred (read B|A as "B given A.") |

Independent | 2 events A & B are independent if the occurrence of one does not affect the probability of the occurrence of the other. |

Dependent | The occurrence of one of them does affect the probability of the occurrence of the other but this does not necessarily mean that one of the events is a cause of the other. |

Formal Multiplication Rule | P(A & B) = P(A) X P(B|A) (if A & B are independent events, P(B|A) is really the same as P(B) |

Intuitive Multiplication Rule | When finding the probability that event A occurs in 1 trial &event B occurs in the next, multiply the probability of event A by the probability of event B, but be sure that the probability of event B takes into account the previous occurrence of event A. |

5% Guideline for Cumbersome Calculations | If a sample size is no more than 5% of the size of the population, treat the selections as being independent (even if the selections are made without replacement, so they are technically dependent.) |

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hfanch24