A fair six-sided die is rolled four times. What is the probability of obtaining at least one six?
Answer and explanation
Correct answer: A. 671 / 1296
- Step 1: Use the complement rule: P(at least one 6) = 1 - P(no sixes). Step 2. P(no six on a single roll) = 5/6. Step 3. P(no six in 4 rolls) = (5/6)^4 = 625 / 1296. Step 4. Complement: 1 - 625 / 1296 = 671 / 1296. Answer: 671 / 1296. Why not the others: 625 / 1296 is the probability of NO sixes; 1/4 naively multiplies 4 by 1/6 without accounting for overlap.
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