To find the probability of rolling two dice and getting a total of 8 dots, we first need to determine the total number of outcomes when rolling two six-sided dice, and then find the number of outcomes that result in a sum of 8.
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Total outcomes: When rolling two dice, each die has 6 sides, so the total number of outcomes is: \[ 6 \times 6 = 36 \]
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Favorable outcomes for a sum of 8: Next, we can list all the combinations of the two dice that yield a total of 8:
- (2, 6)
- (3, 5)
- (4, 4)
- (5, 3)
- (6, 2)
Therefore, the specific outcomes that give a sum of 8 are:
- (2, 6)
- (3, 5)
- (4, 4)
- (5, 3)
- (6, 2)
This gives us a total of 5 favorable outcomes.
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Calculating the probability: The probability \(P\) of rolling a total of 8 is calculated by dividing the number of favorable outcomes by the total number of outcomes: \[ P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{5}{36} \]
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Expressing the probability as a percentage: To express the probability as a percentage, we multiply it by 100: \[ P = \frac{5}{36} \times 100 \approx 13.8889 \]
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Rounding to the nearest hundredth: When we round 13.8889 to the nearest hundredth, we get: \[ 13.89 \]
Thus, the probability of rolling two dice and getting a total of 8 dots showing is 13.89%.