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Probability: Summary of Rules

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1 Probability: Summary of Rules
Rule 1: Complement Rule P(A) + P(Ac) = 1 if Ac represents the complement of A Rule 2B: Additive Rule P(A or B) = P(A) + P(B) if Events A and B are mutually exclusive Note: two events that are complements are always mutually exclusive Rule 3B: Multiplication Rule P(A and B) = P(A)×P(B) if Events A and B are independent

2 Clicker Quiz #8 Maria wants to take French or Spanish, or both. But classes are closed, ands he must apply to enroll in a language class. She has a 60% chance of being admitted to French, a 50% chance of being admitted to Spanish, and a 20% chance of being admitted to both French and Spanish. P(French or Spanish) = _____________________ = _______ = _____ P(French) +P(Spanish) – P(both) – 0.2 0.9 The events “admitted to French” and “admitted to Spanish” are: Mutually exclusive but not independent Independent but not mutually exclusive Both mutually exclusive and independent Neither mutually exclusive nor independent

3 With 50 people in the room…
There are 49 possible pairs with me. P(No match with my birthday) = (364/365)49 = 0.874 There are …+1 = 1225 total possible pairs. P(No match at all) = .030 and we can estimate by (364/365)1225 = .035

4 Probability review Suppose we roll two fair dice, one red and one blue. Let the event A be that we roll the same number on both dice. Let the event B be that the sum of the two dice is even. What is P(A)? What is P(B)? What is P(A and B)? What is P(A or B)? Ans: 6/36 or 1/6 Ans: 18/36 or 1/2 Ans: 1/6 (Note: NOT independent) Ans: 1/2 (Note: NOT mutually exclusive)

5 More probability review
Suppose that you roll a fair 6-sided die until the first occurrence of a 4. What is the probability that the first 4 occurs on the third roll? 1/6 5/6 (5/6) × (5/6) × (1/6) (1/6) × (1/6) × (1/6) (1/6) + (1/6) + (1/6)


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