IPS6eCh04_5bb

# IPS6eCh04_5bb - Probability The Study of Randomness General...

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Probability: The Study of  Randomness General Probability Rules IPS Chapter 4.5 © 2009 W.H. Freeman and Company

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Objectives (IPS Chapter 4.5) General probability rules General addition rules Conditional probability General multiplication rules Tree diagrams Bayes’s rule
General addition rules  General addition rule for any two events A and B: The probability that A occurs, B occurs, or both events occur is: P ( A or B ) = P ( A ) + P ( B ) – P ( A and B ) What is the probability of randomly drawing either an ace or a heart from a deck of 52 playing cards? There are 4 aces in the pack and 13 hearts. However, 1 card is both an ace and a heart. Thus: P (ace or heart) = P (ace) + P (heart) – P (ace and heart) = 4/52 + 13/52 - 1/52 = 16/52 ≈ .3

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Conditional probability Conditional probabilities reflect how the probability of an event can change if we know that some other event has occurred/is occurring. Example: The probability that a cloudy day will result in rain is different if you live in Los Angeles than if you live in Seattle. Our brains effortlessly calculate conditional probabilities, updating our
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IPS6eCh04_5bb - Probability The Study of Randomness General...

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