Upper Level ISEE: A fair sixsided die is rolled twice. What is the probability that the first roll produces a 2 and the second roll does NOT produce a 4? (A) 1/36 (B) 1/18 (C) 5/36 (D) 1/6 (E) 1/3 Solution:
This question deals with the probability of independent events. To summarize: If event A is independent of event B, then the probability of event A occurring AND the probability of event B occurring is P(A) • P(B). First, find the probabilities of each event occurring: P(A), the probability that the first roll produces a 2 = ⅙ P(B), the probability that the second roll does NOT produce a 4 = ⅚ Then, multiply: P(A) • P(B) = ⅙ • ⅚ = 5/36. The answer is (C).
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