Arnav rolls two dice simultaneously. What is the probability of Arnav getting two numbers whose sum is a prime number?
Arnav rolls two dice simultaneously. What is the probability of Arnav getting two numbers whose sum is a prime number?
Solution
When Arnav rolls two dice simultaneously, each die shows a number from 1 to 6.
Total possible outcomes = 6 × 6 = 36
The smallest sum = 1 + 1 = 2
The largest sum = 6 + 6 = 12
Possible sums range from 2 to 12.
A prime number is a number greater than 1 that can only be divided by 1 and itself.
Checking each sum:
- 2 → Prime
- 3 → Prime
- 4 → Not prime
- 5 → Prime
- 6 → Not prime
- 7 → Prime
- 8, 9, 10, 12 → Not prime
- 11 → Prime
Prime sums: 2, 3, 5, 7, 11
For sum = 2: (1,1) → 1 way
For sum = 3: (1,2), (2,1) → 2 ways
For sum = 5: (1,4), (2,3), (3,2), (4,1) → 4 ways
For sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 ways
For sum = 11: (5,6), (6,5) → 2 ways
Total favorable outcomes = 1 + 2 + 4 + 6 + 2 = 15
Probability =
Probability =
Probability =
Therefore, the probability is .
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