Math Foundations

Math Foundations - event. If A and B are independent...

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Conditional probability 11/10/11 Example : RE = roll of a fair 6-face die. So the sample space Ω = {1, 2,394.56}. Let A = prime number occurs = {2, 3.5}. P(A) = 3/6 = 1/2 and B = even number occurs = {2,4,6}. P(B) = 3/6 = 1/2. In a roll of the die, it is observed that B occurred. What is P(A|B)?

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Multiplication rule In general,
Example : There are 100 computers, 75 of which are of brand x. If three computers are selected at random without replacement, what is the probability that each of the selected computers is of brand x. Alternative solution using the counting technique.

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Example : Flip a fair coin repeatedly until a head occurs. If sequence of coin flips is of interest, then it is a RE. The probabilities of each sample point can be calculated by noting that each coin flip is independent of other flips and the product rule for occurrence of multiple independent events. Independent Events Two events A and B are independent if and only if In other words, P(A|B) = P(A), provided B is not a null event, and P(B|A) = P(B), provided A is a not null

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Unformatted text preview: event. If A and B are independent events, so are A' and B, A and B', and A' and B'. In general, non-null events A 1 , A 2 , . .., A n are (statistically) independent if Law of Total Probability A Ω If a job picked at random requires graphics processing, what is the prob. that it is from source 2? P(B 2 |A)? Example : A supercomputer center receives jobs from three different sources. Source % of Jobs % of Jobs that require graphics processing 1 15% 1% 2 35% 5% 3 50% 2% If a job is picked at random, what is the probability that it requires graphics processing? Bayes Theorem Problem 6 , section 7.3 The players of a soccer league are tested for drugs using a special test. With this test, 98% of players taking steroids test positive, and 12% of players not taking steroids test positive. It is estimated that 5% of all players take steroids . What is the probability that a player who tests positive takes steroids?...
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This note was uploaded on 03/21/2012 for the course CS 3333 taught by Professor Boppana during the Fall '11 term at The University of Texas at San Antonio- San Antonio.

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Math Foundations - event. If A and B are independent...

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