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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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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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11 23 13 15 7 10 12 9 TC Q

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1. (C U T U Q) C P(C U T U Q) C = 23/100 2. (CTQ)P (CTQ) = 11/100 3. (C U QT C ) P(C U QT C ) = 29/100 4. (Q)P(Q) = 41/100 5. (TQ) U (QC) U (CT) P(TQ) U (QC) U (CT) = 46/100 6. (TQC C )P(TQC C )= 13/100 7. (TC)P (TC) = 26/100

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TA P 22 73 1431 9 2317 11

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P D G D G 18 10 13 11 15 35 2721

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TD V 73 31 22 14 17 23 9 11

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LH R 25 3 7 5 6 24 18 12

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C P S 177 101 72 137 152 28 122 211

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SB F 20 30 10 40 5 52 35 8

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UW A 30 10 1520 30 5 50 40

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FG S 4 16 8 20 27 12 92 29

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COUNTRYPHYSICSCHEMISTRYPhys/MedTotal United States745190215 United Kingdom21272876 Germany19291563 France117725 Soviet Union91212 Japan4408 TOTAL138119142399 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? 119/399 0.2982 215/399 0.5388 90/142 0.6338 90/215 0.4186

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