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9.7 – Probability of Multiple Events
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Consider the Following: A marble is picked at random from a bag. Without putting the marble back, a second one has chosen. How does this affect the probability? A card is picked at random from a deck of cards. Then a dice is rolled. How does this affect the probability?
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Outcomes of Different Events When the outcome of one event affects the outcome of a second event, we say that the events are dependent. When one outcome of one event does not affect a second event, we say that the events are independent.
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Classify each pair of events as dependent or independent. Probability of Multiple Events a.Spin a spinner. Select a marble from a bag that contains marbles of different colors. Since the two events do not affect each other, they are independent. b.Select a marble from a bag that contains marbles of two colors. Put the marble aside, and select a second marble from the bag. Picking the first marble affects the possible outcome of picking the second marble. So the events are dependent.
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Decide if the following are dependent or independent An expo marker is picked at random from a box and then replaced. A second marker is then grabbed at random. Two dice are rolled at the same time. An Ace is picked from a deck of cards. Without replacing it, a Jack is picked from the deck. Independent Dependent
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How to find the Probability of Two Independent Events If A and B are independent events, the P(A and B) = P(A) * P(B) Ex: If P(A) = ½ and P(B) = 1/3 then P(A and B) =
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Mutually Exclusive Events Two events are mutually exclusive then they can not happen at the same time.
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Probability of Multiple Events Are the events mutually exclusive? Explain. a.rolling an even number or a prime number on a number cube By rolling a 2, you can roll an even number and a prime number at the same time. b.rolling a prime number or a multiple of 6 on a number cube Since 6 is the only multiple of 6 you can roll at a time and it is not a prime number, the events are mutually exclusive. So the events are not mutually exclusive.
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How to find the Probability of Two Mutually Exclusive Events If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)
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Let’s Try One At a restaurant, customers get to choose one of four desserts. About 33% of the customers choose Crème Brule, and about 28% Chocolate Cheese Cake. Natasha is treating herself for pole vaulting nine feet at the meet. What is the probability that she will choose Crème Brule or Chocolate Cheese Cake? Solution:.33 +.28 =.61 = 61% Are the events mutually exclusive? Yes. So: P(A) + P(B)
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