To determine the probability that the sum is odd and the number on one of the dice is a 5 when two 6-sided dice are rolled, let's break down the problem step-by-step:
1. Total Possible Outcomes:
Each die has 6 faces. Therefore, rolling two dice results in:
[tex]\[
6 \times 6 = 36
\][/tex]
This means there are 36 possible outcomes when rolling two 6-sided dice.
2. Outcome Requirements:
We need the sum to be odd and one of the dice to show the number 5.
3. Odd Sums with a 5:
If one die shows 5, we want the sum to be odd. The sum of an odd number and an even number is odd. Thus, we need the other die to show an even number to get an odd sum:
- When the first die is 5: The second die can be 2, 4, or 6.
- When the second die is 5: The first die can be 2, 4, or 6.
4. Favorable Outcomes:
Let's list the pairs where the sum is odd, and one die is 5:
- (5, 2)
- (5, 4)
- (5, 6)
- (2, 5)
- (4, 5)
- (6, 5)
There are 6 such outcomes.
5. Probability Calculation:
The probability of the event is the number of favorable outcomes divided by the total number of possible outcomes:
[tex]\[
\frac{6}{36} = \frac{1}{6}
\][/tex]
Thus, the probability that the sum is odd and one of the dice shows a 5 is [tex]\(\frac{1}{6}\)[/tex]. The correct answer is:
[tex]\[
\boxed{\frac{1}{6}}
\][/tex]
