91Ó°ÊÓ

First, we need to find the number of possible outcomes. In each die, there are 6 possibilities (the numbers 1 to 6). Since there are three dice, the total number of outcomes is: Total Possible Outcomes = 6 (possible numbers on die 1) * 6 (possible numbers on die 2) * 6 (possible numbers on die 3) = \(6^3\)

To have exactly two dice with the same number, we must ensure that the third die shows a different number. We will calculate the favorable outcomes in the following manner: 1. Choose one pair of dice to have the same number. 2. Choose a number to appear on the chosen pair. 3. Choose a number for the third die which is different from the chosen pair. We can calculate the number of ways we can do each step: 1. Choose one pair of dice: There are 3 pairs possible {Die1, Die2}, {Die1, Die3}, {Die2, Die3}. 2. Choose a number to appear on the chosen pair: There are 6 possible numbers (1 to 6). 3. Choose a number for the third die which is different from the chosen pair: As the chosen pair has only one number, we have 5 possibilities for the third die. Now, to calculate the total favorable outcomes, we multiply the number of ways for each step: Favorable outcomes = 3 (possible pairs) * 6 (possible numbers in the pair) * 5 (possible numbers for the third die)

Now that we have the Total Possible Outcomes and Favorable Outcomes, we can calculate the probability as follows: Probability = Favorable Outcomes / Total Possible Outcomes Substituting the values we calculated: Probability = (3 * 6 * 5) / (\(6^3\))

Now, let's simplify the probability: Probability = (3 * 6 * 5) / (\(6^3\)) = 90 / 216 The probability can be further simplified: Probability = 90/216 = 5/12 So, the probability that exactly two of the three dice show the same number is 5/12.