A pair of dice is rolled and the resulting sum is odd. The complement of this event would be the sum of that is a multiple of 3? True or false

I will let you decipher what is meant by "The complement of this event would be the sum of that is a multiple of 3"

However, of the possible 36 sums, 18 will be odd, and 18 will be even
so Prob(odd) = 18/36 = 1/2

take it from there

False. The complement of the event "the resulting sum is odd" would be "the resulting sum is even," not necessarily "the sum is a multiple of 3." The two events are not equivalent.

To determine the answer, we need to consider the possible outcomes when rolling a pair of dice and finding the sum.

First, let's list all the possible outcomes when rolling two dice (each die has six faces numbered from 1 to 6):

1 + 1 = 2
1 + 2 = 3
1 + 3 = 4
1 + 4 = 5
1 + 5 = 6
1 + 6 = 7

2 + 1 = 3
2 + 2 = 4
2 + 3 = 5
2 + 4 = 6
2 + 5 = 7
2 + 6 = 8

3 + 1 = 4
3 + 2 = 5
3 + 3 = 6
3 + 4 = 7
3 + 5 = 8
3 + 6 = 9

4 + 1 = 5
4 + 2 = 6
4 + 3 = 7
4 + 4 = 8
4 + 5 = 9
4 + 6 = 10

5 + 1 = 6
5 + 2 = 7
5 + 3 = 8
5 + 4 = 9
5 + 5 = 10
5 + 6 = 11

6 + 1 = 7
6 + 2 = 8
6 + 3 = 9
6 + 4 = 10
6 + 5 = 11
6 + 6 = 12

Out of these possible sums, the odd sums are: 3, 5, 7, 9, 11.

The complement of an event consists of all the outcomes not included in the original event. So, if we consider the complement of the event "the resulting sum is odd," we need to look at all the outcomes that do not have odd sums. In this case, we need to find the sums that are multiples of 3.

The sums that are multiples of 3 are: 3, 6, 9, 12.

Therefore, the complement of the event "the resulting sum is odd" is the event "the sum is a multiple of 3." Thus, the statement is true.