Discussion
An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice in succession and the number on the top face is recorded each time. The probability that the sum of the two recorded numbers is a prime number is ________
Answer: C
The probability is \(\frac{15}{36}\).
Two rolls give 36 equally likely ordered outcomes, with sums from 2 to 12. The prime sums are 2, 3, 5, 7 and 11. Counting the ordered pairs for each:
- sum 2: (1,1), 1 way;
- sum 3: (1,2), (2,1), 2 ways;
- sum 5: 4 ways;
- sum 7: 6 ways;
- sum 11: (5,6), (6,5), 2 ways.
The total is 1 + 2 + 4 + 6 + 2 = 15, so the probability is 15/36. 3/36 and 13/36 leave out some of the prime sums, and 19/36 includes outcomes whose sum is not prime.
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