Two fair six-sided dice are rolled. Given that the dice do not show the same number, what is the probability that the sum is a prime number?
Answer and explanation
Correct answer: C.
- Step 1: Rolling two dice produces total outcomes, of which are doubles. Removing doubles leaves outcomes with differing numbers.
- Step 2: The prime sums possible are , which occur across pairs in total: ; ; ; ; .
- Step 3: The outcome is a double and must be excluded, leaving valid outcomes. The conditional probability is .
Answer
.
Why not the others: divides without excluding the prime double ; divides by the unconditioned sample space of ; divides ; computes .
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