Two fair 6-sided dice are rolled. Given that the sum of the numbers obtained is greater than , what is the probability that at least one die shows a ?
Answer and explanation
Correct answer: B.
Sum : ( outcomes),
Sum : ( outcomes),
Sum : ( outcomes),
Sum : ( outcome).
Total outcomes with sum : .
( outcomes).
.
Sum : ( outcomes),
Sum : ( outcomes),
Sum : ( outcome).
Total outcomes with sum : .
( outcomes).
.
- Step 1: List all pairs of outcomes whose sum is strictly greater than (the conditioned sample space) :
- Step 2: Identify among these outcomes those where at least one die shows a :
- Step 3: Compute the conditional probability by dividing the favorable count by the conditioned sample space size :
Answer
.
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