Lec_4_STATS - PROBABILITY Important Terms Random Experiment...

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PROBABILITY
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Important Terms Random Experiment – a process leading to an uncertain outcome Basic Outcome – a possible outcome of a random experiment Sample Space – the collection of all possible outcomes of a random experiment Event – any subset of basic outcomes from the sample space
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Coin: 2 outcomes S = {H, T} Die: Six outcomes S = {1,2,3,4,5,6} Cards: 52 outcomes S = {13 of clubs,13 of spades,13 of hearts ,13 of diamonds }
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Let the Sample Space be the collection of all possible outcomes of rolling one die: S = [1, 2, 3, 4, 5, 6] Let A be the event “Number rolled is even” Let B be the event “Number rolled is at least 4” Then A = [2, 4, 6] and B = [4, 5, 6] Examples:
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Important Terms: S = [1, 2, 3, 4, 5, 6] A = [2, 4, 6] B = [4, 5, 6] = C A [1, 3, 5] 6] [4, B A = ! 6] 5, 4, [2, B A = ! C A A [1, 2, 3, 4, 5, 6] S ! = = Complement: Intersection : A and B Union : A or B C A B [5] ! = C B [1, 2, 3] =
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Probability Probability – the chance that an uncertain event will occur P(Heads) = 1/2 P(get a 5) = 1/6 P(get an even number) = 3/6 = 1/2
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Equally Likely Outcomes It’s equally likely to get heads or tails from the toss of a fair coin. It’s equally likely to get any one of six outcomes from the roll of a fair die. When outcomes are equally likely , probabilities for events are easy to find just by counting: However, keep in mind that events are not always equally likely: A skilled basketball player has a better than 50-50 chance of making a free throw.
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Classical Definitions of Probability P ( A ) = number of outcomes in A total number of all possible outcomes = m n True for equally likely outcomes!
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Probability Probability – the chance that an uncertain event will occur - always takes the
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