SOLUTION: Preston buys a bag of cookies that contains 6 chocolate chip cookies, 8 peanut butter cookies, 6 sugar cookies and 7 oatmeal cookies. What is the probability that Preston randomly

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Question 1203987: Preston buys a bag of cookies that contains 6 chocolate chip cookies, 8 peanut butter cookies, 6 sugar cookies and 7 oatmeal cookies. What is the probability that Preston randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie? Express you answer as a reduced fraction.

Answer by math_tutor2020(3817) (Show Source):
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A = 1st selection is sugar cookie
B = 2nd selection is oatmeal cookie

P(A) = (6 sugar)/(6+8+6+7 total)
P(A) = 6/27

P(B given A) = (7 oatmeal)/(27-1 remaining)
P(B given A) = (7 oatmeal)/(26 remaining)
P(B given A) = 7/26

P(A and B) = P(A)*P(B given A)
P(A and B) = (6/27)*(7/26)
P(A and B) = (6*7)/(27*26)
P(A and B) = (2*3*7)/(3*9*2*13)
P(A and B) = 7/(9*13)
P(A and B) = 7/117

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Answer: 7/117