Question:
Two dice are rolled together. The probability that sum of the numbers obtained is atmost 12, is
Two dice are rolled together. The probability that sum of the numbers obtained is atmost 12, is
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An event that is certain to occur is called a sure event, and its probability is always 1.
Since the maximum sum on two dice can never exceed 12, any roll of the dice will satisfy the condition \(S \le 12\).
Recognizing this allows you to choose Option (A) instantly!
Since the maximum sum on two dice can never exceed 12, any roll of the dice will satisfy the condition \(S \le 12\).
Recognizing this allows you to choose Option (A) instantly!
Updated On: Jul 22, 2026
- 1
- 0
- \(\frac{1}{2}\)
- \(\frac{35}{36}\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The topic of this question is Probability.
When two fair six-sided dice are rolled, each die can show any integer from 1 to 6.
The sum of the numbers obtained on both dice will vary from a minimum possible value to a maximum possible value.
We need to find the probability that the sum of the numbers obtained is atmost 12 (i.e., less than or equal to 12).
Step 2: Key Formula or Approach:
The probability of an event \(E\) is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] We will find the range of possible sums when two dice are rolled and determine how many outcomes satisfy our given condition.
Step 3: Detailed Explanation:
• Determine the total number of outcomes when two dice are rolled:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]
• Analyze the range of possible sums:
- The minimum sum occurs when both dice show their smallest number, 1:
\[ \text{Minimum Sum} = 1 + 1 = 2 \] - The maximum sum occurs when both dice show their largest number, 6:
\[ \text{Maximum Sum} = 6 + 6 = 12 \]
• Check the condition "sum is atmost 12":
Atmost 12 means the sum \(S \le 12\).
Since the maximum possible sum when rolling two dice is exactly 12, all 36 possible outcomes will result in a sum that is less than or equal to 12.
Therefore, the number of favorable outcomes is 36.
• Calculate the probability:
\[ P(S \le 12) = \frac{36}{36} = 1 \] Since this event is guaranteed to happen, it is a sure event, which has a probability of exactly 1.
Step 4: Final Answer:
The probability that the sum of the numbers obtained is atmost 12 is 1.
Therefore, the correct option is (A).
The topic of this question is Probability.
When two fair six-sided dice are rolled, each die can show any integer from 1 to 6.
The sum of the numbers obtained on both dice will vary from a minimum possible value to a maximum possible value.
We need to find the probability that the sum of the numbers obtained is atmost 12 (i.e., less than or equal to 12).
Step 2: Key Formula or Approach:
The probability of an event \(E\) is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] We will find the range of possible sums when two dice are rolled and determine how many outcomes satisfy our given condition.
Step 3: Detailed Explanation:
• Determine the total number of outcomes when two dice are rolled:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]
• Analyze the range of possible sums:
- The minimum sum occurs when both dice show their smallest number, 1:
\[ \text{Minimum Sum} = 1 + 1 = 2 \] - The maximum sum occurs when both dice show their largest number, 6:
\[ \text{Maximum Sum} = 6 + 6 = 12 \]
• Check the condition "sum is atmost 12":
Atmost 12 means the sum \(S \le 12\).
Since the maximum possible sum when rolling two dice is exactly 12, all 36 possible outcomes will result in a sum that is less than or equal to 12.
Therefore, the number of favorable outcomes is 36.
• Calculate the probability:
\[ P(S \le 12) = \frac{36}{36} = 1 \] Since this event is guaranteed to happen, it is a sure event, which has a probability of exactly 1.
Step 4: Final Answer:
The probability that the sum of the numbers obtained is atmost 12 is 1.
Therefore, the correct option is (A).
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