The question asks to determine the number of outcomes where the sum of two dice is odd.

When rolling two dice, the sum is odd if:

1. One die shows an odd number, and
2. The other die shows an even number.

The odd numbers on a die are 1, 3, and 5. The even numbers on a die are 2, 4, and 6.

Odd + Even outcomes:

• If Die 1 shows an odd number (1, 3, or 5), Die 2 must show an even number (2, 4, or 6).
• If Die 1 shows an even number (2, 4, or 6), Die 2 must show an odd number (1, 3, or 5).

Let’s count these cases based on this pattern:

Die 1 is odd (1, 3, or 5):

• Die 2 must be even (2, 4, or 6), so each odd number in Die 1 can pair with 3 even numbers in Die 2.
• For Die 1 = 1: (1,2), (1,4), (1,6) → 3 outcomes
• For Die 1 = 3: (3,2), (3,4), (3,6) → 3 outcomes
• For Die 1 = 5: (5,2), (5,4), (5,6) → 3 outcomes

Total for Die 1 being odd: $3 + 3 + 3 = 9$ outcomes.

Die 1 is even (2, 4, or 6):

• Die 2 must be odd (1, 3, or 5), so each even number in Die 1 can pair with 3 odd numbers in Die 2.
• For Die 1 = 2: (2,1), (2,3), (2,5) → 3 outcomes
• For Die 1 = 4: (4,1), (4,3), (4,5) → 3 outcomes
• For Die 1 = 6: (6,1), (6,3), (6,5) → 3 outcomes

Total for Die 1 being even: $3 + 3 + 3 = 9$ outcomes.

Total number of outcomes where the sum is odd:

$9 (\text{Die 1 odd}) + 9 (\text{Die 1 even}) = 18 \text{ outcomes}.$

There are 18 outcomes where the sum of the two dice is odd.

Let me know if you'd like further details or have any questions!

Relative Questions:

1. How do you calculate the probability of getting an odd sum?
2. How would the result change if the dice had a different number of sides?
3. What are the odds of rolling an even sum?
4. How would you calculate outcomes if one die was biased?
5. What is the general formula for determining odd sums with n-sided dice?

Tip: When calculating sums, always remember that the sum of an odd and even number is odd, and the sum of two odd or two even numbers is always even.