05 Introduction to Probability Part 1

Need pr c first compute pr u c 1 pr c 1 030 070 next

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Need P(R ∩ C) First, compute P(R U C) = 1 – P(R’ ∩ C’) = 1 – 0.30 = 0.70 Next, use P(R U C) = P(R) + P(C) – P(R∩C) 0.70 = 0.25 + 0.55 - P(R∩C) P(R∩C) = 0.80 – 0.70 = 0.10 Example: Phillies baseball !
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b) What is the probability that a respondent said that Phillies would beat Cardinals but lose to Reds? Need P(C∩R’) Recall: P(C) = P(C∩R) + P(C∩R’) 0.55 = 0.10 + P(C∩R’) P(C∩R’) = 0.45 Example: Phillies baseball !
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36 Mutually exclusive events Mutually Exclusive = no overlap between events For mutually exclusive events, the intersection is always zero: A C A: the sum is even C: the sum is 7 or 11 2 4 6 8 10 12 7 11 0 C) P(A = 0 C) P(A = 0 C) P(A =
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37 Compound Probability for Mutually Exclusive Events A collection of events, is said to be mutually exclusive if for all pairs For two events For a collection of mutually exclusive events = 0 ) P(E ) P(E ) E P(E ) P(E ) P(E ) E P(E 2 1 2 1 2 1 2 1 + = - + = 0 E E j i = k 2 1 E , , E , E ) P(E ) P(E ) P(E ) E E P(E k 2 1 k 2 1 + + + =
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