Probability

To determine the probability of getting a multiple of 3 as the sum of the numbers on the top faces of two dice, given that their sum is an odd number, we define the following:
Let A be the event that the sum is a multiple of 3 .
Let B be the event that the sum is an odd number.
First, we calculate the total probabilities:
The probability of event A,P(A), is the number of favorable outcomes divided by the total outcomes, i.e., ‌

12

36

.
The probability of event B,P(B), is similarly ‌

18

36

.
Next, we need to determine the probability of both events occurring simultaneously, P(A∩B).
The probability P(A∩B)=‌

6

36

, which represents the outcomes where the sum is both a multiple of 3 and an odd number.
Finally, we calculate the conditional probability of A given B, denoted as P(A∣B) :
P(A∣B)=‌

P(A∩B)

P(B)

=‌

‌ 6 36

18 36

=‌

6

18

=‌

1

3

Therefore, the probability of getting a multiple of 3 as the sum, given that the sum is an odd number, is ‌

1

3

.