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9-7 Probability of Multiple Events

p. 519. 9-7 Probability of Multiple Events. Obj : To be able to find the probabilities of events A and B & A or B. Dependent Event. When the outcome of one event affects the outcome of the second event, the two events are dependent events .

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9-7 Probability of Multiple Events

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  1. p. 519 9-7 Probability of Multiple Events Obj: To be able to find the probabilities of events A and B & A or B.

  2. Dependent Event When the outcome of one event affects the outcome of the second event, the two events are dependent events. Example: A month is selected at random, then a day of that month is selected at random.

  3. Independent Event When the outcome of one event does not affect the outcome of the second event, the two events are independent events. Example: A letter of the alphabet is selected at random, then another letter of the alphabet is selected at random.

  4. Probability of A and B If A and B are independent events, then P(A and B) = P(A)∙P(B)

  5. Independent Events Example 1 What is the probability that if you toss a coin, you will get tails twice in a row? P(A) = P(1st toss is tails) = ½ P(B) = P(2nd toss is tails) = ½ P(A and B) = P(1st and 2nd tosses are tails) = ½ ∙ ½ = ¼

  6. Independent Events Example 2 What is the probability that you pull an ace of clubs out of a deck of cards, replace it and then pull out a spade (any spade)? P(A) = P(1st card is the ace of clubs) = 1/52 P(B) = P(2nd card is a spade) = 1/4 P(A and B) = P(1st card is ace of clubs and 2nd card is a spade ) = 1/52 ∙ 1/4 = 1/208

  7. Probability of A and B If A and B are dependent events, then P(A and B) = P(A)∙P(B after A)

  8. Dependent Events Example 3 What is the probability that you pull an ace of hearts out of a deck of cards, do notreplace it and then pull out an ace (any ace)? P(A) = P(1st card is the ace of hearts) = 1/52 P(B) = P(2nd card is an ace) = 3/51 P(A and B) = P(1st card is ace of hearts and 2nd card is an ace) = 1/52 ∙ 3/51 = 3/2652 = 1/884

  9. Mutually Exclusive When two events cannot happen at the same time, the events are mutually exclusive events. Example: Rolling a 2 or a 3 on a number cube

  10. Probability of A or B If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B) If A and B are not mutually exclusive events, then P(A or B) = P(A) + P(B) – P(A and B)

  11. NOT Mutually Exclusive Mutually Exclusive 3 and odd – can only happen together ONCE (rolling a 3) Example 4 A standard number cube is tossed. Find each probability. a. P(3 or odd) = P(3) + P(odd) – P(3 and odd) = 1/6 + 1/2 – 1/6 = 1/2 b. P(2 or greater than 4) = P(2) + P(greater than 4) = 1/6 + 2/6 = 3/6 = 1/2

  12. Example 5 Suppose you have five books in your book bag. Three are novels, one is a biography, and one is a poetry book. Today, you grab one book out of your bag without looking, and return it later. Tomorrow you do the same thing. What is the probability that you grab a novel both days? Independent Events = 3/5 P(1st book is a novel) P(2nd book is a novel) = 3/5 P(1st and 2nd books are novels) = 3/5 ∙ 3/5 = 9/25

  13. Homework p. 522 #1 – 25 odd

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