alleryTwo dice are rolled. Let E = "sum is 8" and F = "at least one die shows 4". Then P(E|F) equals
A1/11
B1/6
C3/11
D5/11
Answer & Solution
Correct answer: A. 1/11
1. F = {at least one 4}: 11 outcomes among the 36 total two-dice outcomes.
2. E = "sum is 8" = {(2,6),(3,5),(4,4),(5,3),(6,2)}, 5 outcomes.
3. E ∩ F requires sum = 8 AND at least one die = 4: only (4,4). So P(E ∩ F) = 1/36 and P(F) = 11/36.
4. P(E|F) = (1/36) / (11/36) = 1/11.
_Source: syllabus Mathematics, Ch 13 "Probability", §13.2_
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