Answer: There are a total of 6 x 6 = 36 possible outcomes when rolling a pair of dice. We can count the number of outcomes where the sum of the dice is odd or a multiple of 3.
For the sum to be odd, we can have:
A 1 on one die and an even number on the other, or
A 3 on one die and an even number on the other, or
A 5 on one die and an even number on the other, or
A 2 on one die and an odd number on the other, or
A 4 on one die and an odd number on the other, or
A 6 on one die and an odd number on the other.
There are a total of 18 outcomes that satisfy this condition.
For the sum to be a multiple of 3, we can have:
A 1 on one die and a 2 on the other, or
A 1 on one die and a 5 on the other, or
A 2 on one die and a 1 on the other, or
A 2 on one die and a 4 on the other, or
A 3 on one die and a 3 on the other, or
A 4 on one die and a 2 on the other, or
A 4 on one die and a 5 on the other, or
A 5 on one die and a 1 on the other, or
A 5 on one die and a 4 on the other, or
A 6 on one die and a 3 on the other.
There are a total of 10 outcomes that satisfy this condition.
However, we have counted twice the outcomes that satisfy both conditions (i.e., the outcomes where the sum is both odd and a multiple of 3). There are 5 such outcomes: (1,2), (1,5), (5,1), (5,4), and (4,5).
Therefore, the total number of outcomes where the sum of the pair of dice is odd or a multiple of 3 is 18 + 10 - 5 = 23.
The probability of getting one of these outcomes is therefore 23/36.
Explanation: