a) A bag of 11 marbles contains 5 marbles with red on them, 3 with blue on them, 7 with green on them, and 4 with red and green on them. Wwhat is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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a) A bag of 11 marbles contains 5 marbles with red on them, 3 with blue on them, 7 with green
on them, and 4 with red and green on them. What is the probability that a randomly chosen
9.
marble has either green or red on it? Note that these events are not mutually exclusive.
Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
b) Suppose that you and a friend are playing cards and decide to make a bet. If your friend
draws three hearts in succession from a standard deck of 52 cards without replacement, you
give him $40. Otherwise, he pays you $10. What is the expected value of your bet? Round
your answer to the nearest cent, if necessary.
Transcribed Image Text:a) A bag of 11 marbles contains 5 marbles with red on them, 3 with blue on them, 7 with green on them, and 4 with red and green on them. What is the probability that a randomly chosen 9. marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. b) Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws three hearts in succession from a standard deck of 52 cards without replacement, you give him $40. Otherwise, he pays you $10. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.
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