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Two dice are thrown simultaneously. If t...

Two dice are thrown simultaneously. If the probability of the event that sum of numbers shown on the upper face of dice that is greater than 13 is `n/36` then find the value of n.

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To solve the problem, we need to find the probability of the event that the sum of the numbers shown on the upper faces of two dice is greater than 13. ### Step-by-Step Solution: 1. **Understand the Total Outcomes**: When two dice are thrown, each die has 6 faces. Therefore, the total number of possible outcomes when throwing two dice is: \[ \text{Total Outcomes} = 6 \times 6 = 36 \] 2. **Identify the Event**: We need to find the probability of the event where the sum of the numbers on the upper faces of the dice is greater than 13. The maximum sum possible when rolling two dice is: \[ 6 + 6 = 12 \] Since the maximum sum is 12, it is impossible to get a sum greater than 13. 3. **Count the Favorable Outcomes**: Since there are no outcomes where the sum is greater than 13, the number of favorable outcomes is: \[ \text{Favorable Outcomes} = 0 \] 4. **Calculate the Probability**: The probability of an event is given by the formula: \[ P(E) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \] Substituting the values we found: \[ P(E) = \frac{0}{36} = 0 \] 5. **Express the Probability in the Required Form**: The problem states that the probability can be expressed as \( \frac{n}{36} \). Since we found that the probability is 0, we can write: \[ 0 = \frac{0}{36} \] Thus, \( n = 0 \). ### Final Answer: The value of \( n \) is \( 0 \).
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