You have three dice. What is the probability to find rolling two same number?
let's pick one specific case
e.g. two 3's and the third one different
33?
the probability of that is 1/6 * 1/6 * 5/6
but there are 3 ways for 33? to turn up
33?,3?3, and ?33
but there are 6 such cases that could happen
two 1's, two 2's etc
so the prob. is 6(1/6)(1/6)(5/6)(3) = 5/12
Thank you so much.
To find the probability of rolling two of the same number when rolling three dice, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the total number of possible outcomes when rolling three dice. Each die has six sides, so the total number of outcomes for one die is 6. Since we are rolling three dice, we can multiply the number of outcomes for each die together: 6 * 6 * 6 = 216.
Next, let's determine the number of favorable outcomes, which is the number of ways we can roll two of the same number. There are three potential scenarios for this:
1. Choosing two of the same number from the first to the second die. We have six possible numbers (1-6) to choose from, so there are 6 ways to select the matching numbers. Once we have selected the matching number, the third die can show any number from 1 to 6. Therefore, there are 6 * 6 = 36 favorable outcomes for this scenario.
2. Choosing two of the same number from the first to the third die. Again, we have 6 possible numbers to choose from, resulting in 6 * 6 = 36 favorable outcomes.
3. Choosing two of the same number from the second to the third die. We still have 6 possible numbers to choose from, resulting in 6 * 6 = 36 favorable outcomes.
To find the total number of favorable outcomes, we sum up the favorable outcomes from each scenario: 36 + 36 + 36 = 108.
Finally, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes: 108 / 216 = 0.5.
Therefore, the probability of rolling two of the same number when rolling three dice is 0.5 or 50%.