Probability of Total Being Divisible by 3 or 4

To find the probability that the total of two dice is divisible by 3 or 4, we need to consider all the possible outcomes and count the favorable outcomes.

Possible outcomes:
When two dice are tossed, the total number of outcomes is 36 (since each die has 6 possible outcomes: 1, 2, 3, 4, 5, or 6). The possible outcomes can be represented by a sample space as follows:

{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

Favorable outcomes:
Now, we need to determine the favorable outcomes where the total is divisible by 3 or 4.

Divisible by 3:
When two numbers are added and the sum is divisible by 3, the possible combinations are:
(1,2), (2,1), (1,5), (5,1), (2,4), (4,2), (1, 1), (4,5), (5,4), (2, 2), (5,5), (4,4), (3, 6), (6, 3), (3, 3), (6, 6)

Divisible by 4:
When two numbers are added and the sum is divisible by 4, the possible combinations are:
(1, 3), (3, 1), (2, 2), (2, 6), (6, 2), (3, 5), (5, 3), (4, 4), (4, 6), (6, 4), (5, 5), (6, 6)

Finding the probability:
To calculate the probability, we need to divide the number of favorable outcomes by the total number of possible outcomes.

Number of favorable outcomes = 27 (combining the favorable outcomes for divisibility by 3 and 4)
Total number of possible outcomes = 36

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 27 / 36
Probability = 0.75 or 75%

Therefore, the probability that the total of two dice is divisible by 3 or 4 is 0.75 or 75%.

20/36