Lec2 - Probability Pr{ E 1 or E 2 } = Pr{ E 1 } + Pr{ E 2 }...

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Unformatted text preview: Probability Pr{ E 1 or E 2 } = Pr{ E 1 } + Pr{ E 2 } - Pr{ E 1 and E 2 } 40 km Democratic Republic of the Congo Uganda Rwanda Virunga volcanoes (430 km , 380 gorillas) Bwindi Impenetrable National Park (320 km , 300 gorillas) Probability Pr{ E 1 or E 2 } = Pr{ E 1 } + Pr{ E 2 } - Pr{ E 1 and E 2 } Random experiment Assumption : the experiment can be repeated indefnitely under essentially the same conditions Outcome of the experiment = Event Ex1: at least one 6 is obtained Ex2: the total is 10 Ex3: no 1 is obtained Defnition : an experiment which outcome cannot be predicted with certainty Probability Definition : a numerical quantity that expresses the likelihood of an event Pr{ E } Probability of an event E 0 Pr{ E } 1 The event is guaranteed to happen The event will never occur Each time the operation occurs, event E either occurs or does not occur Probability only makes sense if there is an element of uncertainty in the operation (random experiment) Event E : Heads Operation Tossing the coin once Pr{E} = 0.5 Coin tossing More Probability Event E : 3 heads in a row Operation Tossing the coin 3 times Pr{E} = 0.125 --------------------------------------------- Operation Tossing the coin 4 times Pr{E} = 0.188 --------------------------------------------- Operation Tossing the coin 5 times Pr{E} = 0.25 Coin tossing Probability and random sampling Drosophila melanogaster 30% black 70% gray E : Sampled fly is black P{ E } = 0.3 The probability of randomly choosing a certain kind of individual is equal to the proportion of that kind in the population Probability helps us describe the outcome of a random sample . Frequency interpretation of probability E : Sampled fly is black P{ E } = 0.3 4/10 = 0.4 7/20 = 0.35 29/100 = 0.29 P{ E } # times E occurs # times perform operation eventually The probability can be thought of as the relative frequency of occurrences of E in an indefinitely long series of repeated chance operations. Lets try it E : Heads Operation: One coin flip P{ E } = 0.5 What about the first two rows?...
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This note was uploaded on 11/04/2009 for the course BIO 50935 taught by Professor Bryant during the Fall '09 term at University of Texas at Austin.

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Lec2 - Probability Pr{ E 1 or E 2 } = Pr{ E 1 } + Pr{ E 2 }...

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