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Upper Level ISEE:
A fair six-sided die is rolled twice. What is the probability that the first roll produces a 2 and the second roll does NOT produce a 4?
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).