4_5_Handout - 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 if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) + P(B) This is the addition rule for disjoint events . 4) The complement of any event A is the event that A does not occur, written as A c . The complement rule states that P(A c ) = 1 – P(A) 5) Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent, P(A and B) = P(A)P(B) This is the multiplication rule for independent events . 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) Figure 4.18 EX) 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)
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4_5_Handout - 4.5 General Probability Rules Previous...

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