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**12.4 Probability of Compound Events**

Vocabulary 12.4 Concurrent Events Compound: two events that are considered together Overlapping: events with one or more outcomes in common Disjoint: events with no outcomes in common Complement: Ā is the complement of A which is all outcomes not in A

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Compound Events Compound: two events that are considered together on one trial Overlapping events have one or more outcomes in common Disjoint events have no outcomes in common (often called mutually exclusive) Compound events will generally use the word ‘or’. (What is the probability of this or that happening when I …)

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Overlapping Events Overlapping events have one or more outcomes in common Ex: a number thrown on a fair 6-sided die is < 4 or it is odd (1 and 3 satisfy both conditions) Ex: A card is drawn and it is a number (like 4) or a suit (like hearts)

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**Probability of Overlapping Events**

If A and B are two overlapping events, then the probability of A or B is: P(A or B) = P(A) + P(B) – P(A and B) = (Each possibility must be accounted for once and only once) A B A B A & B

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SAT Test Practice A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a face card or a spade? = A. ³/₅₂ B. ¹⅟₂₆ C. ²⁵/₅₂ D. ⁷/₁₂ Deck of Cards Deck of Cards Deck of Cards Deck of Cards Spade Face card Face card Spade Both

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Disjoint Events Disjoint events have no outcomes in common (often called mutually exclusive) Ex: A fair 12-sided die is rolled. What is the probability it will land with a 5 or a 9 up? Ex: a disk is drawn from a cup of 5 red, 6 blue, 4 green, and 5 yellow. What is the probability that the disk is yellow or green?

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**Probability of Disjoint Events**

If A and B are two disjoint events, then the probability of A or B is: P(A or B) = P(A) + P(B) = (Each possibility must be accounted for once and only once) A B A B

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**Find Probability of Disjoint Events**

A card is randomly selected from a standard deck of 52 cards, What is the probability that it is a 10 or a face card? = Deck of Cards Deck of Cards Deck of Cards Face card Face card 10 10

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**Use a formula to find P(A and B)**

Out of 200 students in a senior class, 113 students are either varsity athletes or on the honor roll. There are 74 seniors who are varsity athletes and 51 seniors who are on the honor roll. What is the probability that a randomly selected senior is both a varsity athlete and on the honor roll? = Seniors Honor Role Varsity Athlete Honor Role Varsity Athlete Both

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Try these: A card is randomly drawn from a standard deck of 52 cards. Find the probability of the given event. Selecting an ace or an eight Selecting a 10 or a diamond In the senior class example, suppose 32 seniors are in band and 64 seniors are in the band or on the honor roll. What is the probability that a randomly selected senior is both in the band and on the honor roll?

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**Compliments Ā is the compliment of A, which is all outcomes not in A.**

The probability of Ā is: P(Ā) = 1 – P(A) Ā A is everything in the pink circle. Ā is everything in the blue region A

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**Find Probabilities of compliments**

When two six sided dice are rolled, there are 36 possible outcomes. Find the probability of: The sum is not 6 P(sum not 6) = 1 – P(sum is 6) The sum is less than or equal to 9 P(sum ≤ 9) = 1 –[P(sum is 10)+P(sum is 11)+P(sum is 12)]

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**Use a Compliment in real life**

A restaurant gives a free fortune cookie to every guest. The restaurant claims there are 500 different messages hidden inside the fortune cookies. What is the probability that a group of 5 people receive at least 2 fortune cookies with the same message? P(at least 2 fortunes match) = 1 – P(0 matches)

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Homework HW 48: pg 727, odd, all

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