Question

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 ________

• A. \( \dfrac{3}{36} \)
• B. \( \dfrac{13}{36} \)
• C. \( \dfrac{15}{36} \)
• D. \( \dfrac{19}{36} \)

Hint:

List the prime sums possible between 2 and 12, count outcomes for each, and divide by 36.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
A fair six sided die is rolled twice, so the total number of equally likely outcomes is 6 multiplied by 6, which is 36 ordered pairs of the form first roll, second roll. We need the probability that the sum of the two numbers rolled is a prime number.
Step 2: Key Formula or Approach:
The possible sums when rolling two dice range from 2, the smallest possible sum, up to 12, the largest possible sum. We first list which of these sums are prime numbers, then count how many of the 36 ordered outcomes give each of those prime sums, add up the counts, and divide by 36 to get the required probability.
Step 3: Detailed Explanation:
The prime numbers between 2 and 12 are 2, 3, 5, 7 and 11.
Sum equal to 2 occurs only as (1,1), giving 1 outcome.
Sum equal to 3 occurs as (1,2) and (2,1), giving 2 outcomes.
Sum equal to 5 occurs as (1,4), (2,3), (3,2) and (4,1), giving 4 outcomes.
Sum equal to 7 occurs as (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1), giving 6 outcomes.
Sum equal to 11 occurs as (5,6) and (6,5), giving 2 outcomes.
Adding these counts together gives 1 + 2 + 4 + 6 + 2 = 15 favourable outcomes out of the 36 total equally likely outcomes.
Step 4: Final Answer:
The required probability is 15 divided by 36.
\[ oxed{\dfrac{15}{36}} \]