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**Unformatted text preview: **50 CHAPTER 3. PROBABILITY TOPICS c. P ( G | E ) = d. P ( G AND E ) = e. P ( G OR E ) = f. Are G and E mutually exclusive? Justify your answer numerically. Exercise 3.2 Refer to the previous problem. Suppose that this time you randomly draw two cards, one at a time, and with replacement . G 1 = first card is green G 2 = second card is green a. Draw a tree diagram of the situation. b. P ( G 1 AND G 2 ) = c. P ( at least one green ) = d. P ( G 2 | G 1 ) = e. Are G 2 and G 1 independent events? Explain why or why not. Exercise 3.3 (Solution on p. 63.) Refer to the previous problems. Suppose that this time you randomly draw two cards, one at a time, and without replacement . G 1 = first card is green G 2 = second card is green a. Draw a tree diagram of the situation. b &gt; . P ( G 1 AND G 2 ) = c. P(at least one green) = d. P ( G 2 | G 1 ) = e. Are G 2 and G 1 independent events? Explain why or why not. Exercise 3.4 Roll two fair dice. Each die has 6 faces. a. List the sample space. b. Let A be the event that either a 3 or 4 is rolled first, followed by an even number. Find P ( A ) . c. Let B be the event that the sum of the two rolls is at most 7. Find P ( B ) . d. In words, explain what P ( A | B ) represents. Find P ( A | B ) . e. Are A and B mutually exclusive events? Explain your answer in 1 - 3 complete sentences, including numerical justification....

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