To determine the probability that the sum of two number cubes (each numbered from 1 to 6) is equal to 6, we need to follow these steps:
1. Calculate the total number of possible outcomes:
Each cube has 6 faces, and each face is equally likely to land face up. Since Leon is tossing two dice, we need to consider all possible outcomes of a roll of two dice. Each die is independent of the other, so we multiply the number of outcomes for one die by the number of outcomes for the other die:
[tex]\[
\text{Total number of possible outcomes} = 6 \times 6 = 36
\][/tex]
Thus, there are 36 possible outcomes when two dice are tossed.
2. Identify the favorable outcomes where the sum is 6:
We need to find the pairs of numbers on the dice that add up to 6. The pairs are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)
By counting these pairs, we see that there are 5 favorable outcomes.
3. Calculate the probability:
The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability [tex]\(P\)[/tex] that the sum of the two dice is 6 is:
[tex]\[
P(\text{sum } = 6) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{5}{36}
\][/tex]
So, the probability that Leon will toss a sum of 6 is:
[tex]\[
\boxed{\frac{5}{36}}
\][/tex]
