Official Guide Explanation:
Problem Solving #174




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Solution and Metadata

Question: 174
Page: 177
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Discrete Probability >
Category 2: Word Problems > Sets >

Explanation: The key words in this question are "at least." When you see those words, turn the question upside down: instead of solving for the probability of what they're asking for, solve for the opposite. In this case, the opposite of "at least one tail" is "all heads." The probability of any one toss turning up heads is (1/2), so the probability of three consecutive tosses coming up heads is ((1/2))((1/2))((1/2)) = (1/8). Since we found the opposite of what we were looking for, we need to subtract our answer from 1, as follows: 1 - (1/8) = (7/8), choice (D).

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