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14111cn7.15-17 - was chosen from the bag what is the...

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c Kendra Kilmer October 11, 2011 Section 7.6 - Bayes’ Theorem Example 1 : If we are given information about P ( F | E ) , can we find P ( E | F ) ? Definition : The above formula is known as Bayes’ Theorem . Example 2 : We are to choose a marble from a cup or a bowl. We flip a fair coin to decide whether to choose from the cup or the bowl. The bowl contains 1 red and 2 green marbles. The cup contains 3 red and 2 green marbles. What is the probability that a marble came from the bowl given that it is red? 15
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c Kendra Kilmer October 11, 2011 Example 3: A crate contains 7 basketballs and 4 footballs. A bag contains 4 basketballs and 2 footballs. A ball is drawn at random from the crate and put in the bag. A ball is then drawn from the bag. Given that a basketball
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Unformatted text preview: was chosen from the bag, what is the probability that a football was drawn from the crate? Example 4 : Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a face card given that the second card is an ace? 16 c ± Kendra Kilmer October 11, 2011 Example 5 : Complete the following tree diagram and use it to answer the following questions: a) Find P ( E ) . b) Find P ( A ∪ D ) . c) Find P ( B | E ) . d) Are E and B independent events? Section 7.6 Highly Suggested Homework Problems: 7, 9, 13, 15, 17, 19, 21, 33, 42, 50 17...
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