Title: CAT 2021 Quant Slot 2 Solution (English Explanation)
Problem Statement:
A game involves rolling two standard six-sided dice. What is the probability that the sum of the two dice is a prime number?
Solution:
Total Possible Outcomes:
Each die has 6 faces. When rolling two dice, the total number of possible outcomes is:
[
6 \times 6 = 36
]
Prime Numbers Possible as Sums:
The possible sums of two dice range from 2 to 12. Prime numbers in this range are: 2, 3, 5, 7, 11.
Favorable Outcomes for Each Prime Sum:
Sum = 2: Only (1,1) → 1 outcome
Sum = 3: (1,2), (2,1) → 2 outcomes
Sum = 5: (1,4), (2,3), (3,2), (4,1) → 4 outcomes
Sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 outcomes
Sum = 11: (5,6), (6,5) → 2 outcomes
Total favorable outcomes = (1 + 2 + 4 + 6 + 2 = 15).
Probability Calculation:
[
\text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{15}{36} = \frac{5}{12}
]
Answer:
The probability is (\boxed{\dfrac{5}{12}}).
Key Takeaways:
Identify all prime sums within the possible range.
List favorable outcomes systematically to avoid missing combinations.
Simplify fractions to their lowest terms for final answers.
Let me know if you need further clarification! 😊
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