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# handout_4_5 - 4.5 General Probability Rules Previous...

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4.5 General Probability Rules Previous Probability Rules 1) The probability P(A) of any event A satisfies 0 P(A) 1. 2) All possible outcomes together must have probability 1. P(S) = 1. 3) Two events A and B are disjoint P(A or B) = P(A) + P(B) 4) The complement rule states that→ P(A c ) = 1 – P(A) 5) Two events A and B are independent P(A and B) = P(A)P(B) General addition rules The union of any collection of events is the event that at least one of the collection occurs. Addition rule for disjoint events (Figure 4.16) If events A, B, and C are disjoint in the sense that no two have any outcomes in common, then P (one or more of A, B, C) = P(A) + P(B) + P(C) This rule extends to any number of disjoint events.

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General addition rule for unions of two events For any two events A and B, P(A or B) = P(A) + P(B) – P(A and B) EX 1) random phenomenon→ toss a die (A- roll a 1, B- roll an odd #) P(A or B) = P(get 1, 3, or 5) = 0.5 P(A or B) = P(A) + P(B) – P(A and B) P(A or B) = (1/6) + (3/6) – (1/6) = 0.5 before→ P(A or B) = P(A) + P(B) (A, B disjoint) now→ P(A or B) = P(A) + P(B) – P(A and B) (A, B can have overlap) EX 2) random phenomenon→ toss a die (A- roll a 1, B- roll a 2) A, B disjoint
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handout_4_5 - 4.5 General Probability Rules Previous...

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