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GENERAL PROBABILITY RULES

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General addition rule P(A or B) = P(A) + P(B) – P(A and B) Addition rule for disjoint events P(one or more of A, B, C) = P(A) + P(B) + P(C) Multiplication rule for independent events P(A and B) = P(A)P(B) Review of Previous Rules

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Conditional probability – the probability of one event under the condition that we know another event. The | can be interpreted as given the information that

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General addition rule P(A or B) = P(A) + P(B) – P(A and B) P(A U B) = P(A) + P(B) – P(A B) General multiplication rule P(A and B) = P(A)P(B given A) P(A B) = P(A)P(B|A) When P(A) > 0, Testing for independence : Two events A and B are independent if P(B|A) = P(B)

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Two events A and B are independent if P(B|A) = P(B) Think back to your last quiz. When rolling a die and then flipping a coin, let event A be getting a 1 or 2 on the roll of the die. Let event B be getting an even number on the die. Are A and B independent? P(B|A) = (2/12)/(4/12) = ½ P(B) = 6/12 = ½ Therefore, A and B are independent.

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A B BLUE REPRESENTS DESIGNATED AREA

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A B

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A B

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A B

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A B

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A B

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A B

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A B

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Musical styles other than rock and pop are becoming more popular. A survey of college students find that 40% like country music, 30% like gospel music, and 10% like both. What is the conditional probability that a student likes gospel music if we know that he/she likes country music? C G 10%30%20% Conditional Probability P(G|C) = 0.1/0.4=0.25

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Musical styles other than rock and pop are becoming more popular. A survey of college students find that 40% like country music, 30% like gospel music, and 10% like both. What is the conditional probability that a student who does not like country music likes gospel music? C G 10%30%20% Conditional Probability P(G|C C ) = 0.2/0.6=1/3

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TC Q

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1. (C U T U Q) C P(C U T U Q) C = 23/ (CTQ)P (CTQ) = 11/ (C U QT C ) P(C U QT C ) = 29/ (Q)P(Q) = 41/ (TQ) U (QC) U (CT) P(TQ) U (QC) U (CT) = 46/ (TQC C )P(TQC C )= 13/ (TC)P (TC) = 26/100

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TA P

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P D G D G

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TD V

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LH R

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C P S

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SB F

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UW A

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FG S

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COUNTRYPHYSICSCHEMISTRYPhys/MedTotal United States United Kingdom Germany France Soviet Union91212 Japan4408 TOTAL If a laureate is selected at random, what is the probability that: a)his or her award is in chemistry? b)the award was won by someone working in the US? c)the awardee was working in the US, given the award was for phys./med? d)the award was for phys./med., given that the awardee was working in the US? 119/ / / /

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