Two dice, one red and one white are rolled. What is the probability that the white die turns up a smaller number than the red die ?

15/36 = 5/12

(white, red)

----> 12 13 14 15 16 (5 of them
----> 23 24 25 26 (4 of them)
----> 34 35 36 (3 of them)
----> 45 46 (2 of them)
----> 56 just one

so 5+4+3+2+1 = 15

prob(your event) = 15/36

To find the probability that the white die turns up a smaller number than the red die, you need to determine the total number of possible outcomes and the number of favorable outcomes.

Step 1: Determine the total number of possible outcomes.
When rolling two dice, there are 6 possible outcomes for each die. Since there are two dice, the total number of possible outcomes is 6 × 6 = 36.

Step 2: Determine the number of favorable outcomes.
To calculate the number of favorable outcomes, you can use a table or visualize the possibilities visually. Here's a table to help you:

| Red Die
White Die| 1 | 2 | 3 | 4 | 5 | 6 |
--------------------------------
1 | X | X | X | X | X | X |
2 | | X | X | X | X | X |
3 | | | X | X | X | X |
4 | | | | X | X | X |
5 | | | | | X | X |
6 | | | | | | X |

In the table, the X represents the instances where the white die turns up a smaller number than the red die. Counting the X's, we find that there are 15 favorable outcomes.

Step 3: Calculate the probability.
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes. In this case, the probability is 15/36, which simplifies to 5/12.

Therefore, the probability that the white die turns up a smaller number than the red die is 5/12 or approximately 0.4167.