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Vocabulary

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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Vocabulary

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  1. 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

  2. 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 …)

  3. 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)

  4. 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

  5. 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

  6. 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?

  7. 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

  8. 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

  9. 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

  10. 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?

  11. 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

  12. 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)]

  13. 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)

  14. Homework • HW 48: pg 727, 17-27 odd, 28-41 all

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