Official Guide Explanation:
Problem Solving #214




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Solution and Metadata

Question: 214
Page: 183
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Discrete Probability >
Category 2: Word Problems > Sets >
Category 3: Arithmetic > Fractions >

Explanation: If Xavier and Yvonne, but not Zelda, solve the problem, there are three events that must occur, each of which have their own probability. The probability that Xavier sovles the problem is (1/4) , that Yvonne solves the problem, (1/2), and that Zelda doesn't solve the problem, 1 - (5/8) = (3/8). The probability of multiple independent events occuring is the product of the individual probabilities, so we're looking for ((1/4))((1/2))((3/8)) = ((1(1)(3))/((4)(2)(8))) = (3/64) , choice (E).

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