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.,
.
The probability of event
B,P(B), is similarly
.
Next, we need to determine the probability of both events occurring simultaneously,
P(A∩B).
The probability
P(A∩B)=, 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)====Therefore, the probability of getting a multiple of 3 as the sum, given that the sum is an odd number, is
.
