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Aim: Or Probabilities Course: Math Lit. Do Now: Aim: What are Or Probabilities? What is the probability of spinning a number greater than 8 or an odd number?

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Aim: Or Probabilities Course: Math Lit. Probability of A or B What is the probability of spinning a number greater than 8 or an odd number? Count the number of successes for n > 8 n - odd not yet counted 9, 10, 11, , 3, 5, 7 4 {1, 3, 5, 7, 9, 10, 11, 12} > 8 odd =

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Aim: Or Probabilities Course: Math Lit. Union Region I Region II Region IV AB Reg. III U The union of sets A and B is region II, II & IV. or is the term used to describe union The union of sets A and B, denoted by A B, is the set consisting of all elements of A or B or both. A B = {x|x A OR x B}

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Aim: Or Probabilities Course: Math Lit. Union of Do Now > 8 = {9, 10, 11, 12} U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} odd = {1, 3, 5, 7, 9, 11} > odd U 1, 3, 5, 7,10, 12 2, 4, 6, 8 A B = {1, 3, 5, 7, 9, 10, 11, 12} n(A B) = 8

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Aim: Or Probabilities Course: Math Lit. Independent Events Mutually exclusive – two events A & B are mutually exclusive if they can not occur at the same time. That is, A and B are mutually exclusive when A B = An outcome for A or B is in one or the other. If the events are mutually exclusive the P(A or B) = P(A) + P(B) If one card is randomly selected from a deck of cards, what is the probability of selecting a king or a queen? mutually exclusive? yes

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Aim: Or Probabilities Course: Math Lit. Or Probabilities Not Mutually Exclusive From a standard deck you randomly select one card. What is the probability of selecting a diamond or a face card? mutually exclusive? no common elements A B n(A B) = 3 {K, Q, J } P( or fcd) =

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Aim: Or Probabilities Course: Math Lit. Probability of (A or B) Example: Find the probability of rolling a die and getting a number that is odd or greater than 2. {1,3,5}{3,4,5,6} successes P(A or B) = P(A) + P(B) - P(A and B) P(A B) = P(A) + P(B) - P(A B) P(A B) = n(A) + n(B) - n(A B) n(S) n(S) n(S) If A and B are not mutually exclusive events, then

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Aim: Or Probabilities Course: Math Lit. Model Problem Find the probability of rolling a die and getting a number that is odd or greater than odd > 2 P(odd) = 3/6P(> 2) = 4/6 A B = {1, 3, 4, 5, 6} n(A B) = 5 n(U) = 6

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Aim: Or Probabilities Course: Math Lit. Model Problem In a group of 50 students, 23 take math, 11 take psychology, and 7 take both. If one student is selected at random, find the probability that the student takes math or psychology P(A B) = P(A) + P(B) - P(A B) MPsy

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Aim: Or Probabilities Course: Math Lit. Model Problems 1. A card is drawn from a standard deck of 52. Find P(Ace or jack) 4 52 P(ace) = 4 52 P(jack) = P(ace or jack) = = 2. A card is drawn from a standard deck of 52. Find P(king or face card) 4 52 P(king) = P(face) = P(king or face) = _ = mutually exclusive not mutually exclusive

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Aim: Or Probabilities Course: Math Lit. Model Problems In drawing a card from the deck at random, find the probability that the card is: A. A red king B. A 10 or an ace C. A jack or a club A red king must be red and a king P(red and king) = 2 52 There are 4 jacks and 13 clubs, but one of the cards is both (jack of clubs) P(jacks or clubs) = _ = 10s and aces have no common outcomes P(10s or aces) = _ = 8 P(A and B) = P(A) · P(B) P(A B) = P(A) + P(B) - P(A B) mutually exclusive not mutually exclusive

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Aim: Or Probabilities Course: Math Lit. Model Problems Based on the table below, if one person is randomly selected from the US military, find the probability that this person is in the Army or is a woman. Air Force ArmyMarinesNavyTotal Male Female Total Active Duty US Military Personnel, in 000s P(A B) = P(A) + P(B) - P(A B) P(Army Female) = P(A) + P(F) - P(A F) not mutually exclusive

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Aim: Or Probabilities Course: Math Lit. 1. The probability of an impossible event is The probability of an event that is certain to occur is The probability of an event E must be greater than or equal to 0 and less that or equal to P(A and B) = n(A B) n(S) 5. P(A or B) = P(A) + P(B) - P(A B) 6. P(Not A) = 1 - P(A) 7. The probability of any even is equal to the sum of the probabilities of the singleton outcomes in the event. 8. The sum of the probabilities of all possible singleton outcomes for any sample space must always equal 1. Probability Rules

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Aim: Or Probabilities Course: Math Lit. Model Problems Five more men than women are riding a bus as passengers. The probability that a man will be the first passenger to leave the bus is 2/3. How many passengers on the bus are men, and how many are women? x = number of women x + 5 = number of men 2x + 5 = number of passengers P(man) = Number of men Number of passengers x + 5 2x = 4x + 10 = 3x + 15 x = 5 x + 5 =

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Aim: Or Probabilities Course: Math Lit. The Product Rule

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