Find the indicated probability. Round your answer to 6 decimal places when necessary.
-When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that the sum is a multiple of 3 or greater than 8.

Question

Quizplus · Accepted Answer

To find the probability that the sum is a multiple of 3 or greater than 8, we first identify the outcomes that satisfy each condition and then combine them, making sure not to double-count any outcomes that satisfy both conditions.Multiples of 3: The sums that are multiples of 3 are 3, 6, 9, and 12. The outcomes that give these sums are:- For 3: (1,2), (2,1)- For 6: (1,5), (2,4), (3,3), (4,2), (5,1)- For 9: (3,6), (4,5), (5,4), (6,3)- For 12: (6,6)This gives us 12 outcomes.Sums greater than 8: The sums greater than 8 are 9, 10, 11, and 12. The outcomes that give these sums are:- For 9: (3,6), (4,5), (5,4), (6,3) (already counted in multiples of 3)- For 10: (4,6), (5,5), (6,4)- For 11: (5,6), (6,5)- For 12: (6,6) (already counted in multiples of 3)This gives us 6 additional outcomes, not counting the ones already included in the multiples of 3.Adding the outcomes together, we have 12 (for multiples of 3) + 6 (for sums greater than 8, without double-counting) = 18 outcomes. Since there are 36 possible outcomes when rolling two dice, the probability is $ \frac{18}{36} = \frac{1}{2} $. However, this calculation mistakenly includes an incorrect count. Correctly identifying and counting the outcomes gives us:Multiples of 3 (correctly counted): 12 outcomes.Sums greater than 8 (correctly counted, without double-counting): 10 - (4,6), (5,5), (6,4); 11 - (5,6), (6,5); 12 - (6,6) gives us 5 unique outcomes not already counted in the multiples of 3.Correctly combining these, we actually have 12 (multiples of 3) + 5 (unique outcomes greater than 8) = 17 outcomes that satisfy at least one of the conditions. Therefore, the probability is $ \frac{17}{36} $.

Find the Indicated Probability 13\frac { 1 } { 3 }31​

Find the Indicated Probability $\frac { 1 } { 3 }$