Solving the Probability of Getting the Same Number on Two of Three Dice

 Three dice are thrown. What is the probability the same number appears on exactly two of the three dice?

Throwing three dice is a popular game, but calculating the probability of getting the same number on exactly two of them can be challenging. However, with a little bit of mathematical reasoning, the solution to this problem can be obtained.

The probability of getting the same number on two of three dice can be calculated by considering the different ways the dice can fall and the number of successful outcomes. The number of possible outcomes when throwing three dice is 6 x 6 x 6 = 216. To get the same number on two of the dice, we can pick two dice and assign the same number to them, and then choose any number for the third die.

Therefore, the number of successful outcomes can be calculated as follows:

6 ways to pick the number that appears on two dice * 6 ways to pick the number for the third die = 36

Dividing the number of successful outcomes by the total number of possible outcomes, we get the probability of getting the same number on two of three dice as:

36 / 216 = 1/6

Therefore, the probability of getting the same number on exactly two of the three dice is 1/6 or approximately 0.17.