Let's determine the probability that the sum of the two dice will be a multiple of 5.
### Step 1: List All Possible Outcomes
When two fair dice, each numbered 1 to 6, are thrown, the total number of possible outcomes can be represented as a 6x6 grid where each cell represents a sum of two dice. There are [tex]\(6 \times 6 = 36\)[/tex] possible outcomes.
### Step 2: Identify Favorable Outcomes
We need to find the sum of two numbers that is a multiple of 5. The multiples of 5 that can appear as sums of the dice are 5, 10.
Now let's list the combinations of dice values that result in these sums:
- Sum = 5:
- (1, 4)
- (2, 3)
- (3, 2)
- (4, 1)
- Sum = 10:
- (4, 6)
- (5, 5)
- (6, 4)
From this, we can tally up the total number of favorable outcomes:
- Sum = 5: 4 outcomes
- Sum = 10: 3 outcomes
Thus, there are [tex]\(4 + 3 = 7\)[/tex] favorable outcomes.
### Step 3: Calculate the Probability
The probability [tex]\( P \)[/tex] of getting a sum that is a multiple of 5 is the ratio of the number of favorable outcomes to the total number of possible outcomes.
[tex]\[
P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{7}{36}
\][/tex]
Finally, converting this ratio to its decimal form, we get:
[tex]\[
P \approx 0.19444444444444445
\][/tex]
So, the probability that the sum of the numbers on two dice is a multiple of 5 is [tex]\( \frac{7}{36} \approx 0.1944 \)[/tex] or roughly 19.44%.
