Using the sum rule of probability determine the probability

Using the sum rule of probability, determine the probability of rolling two dice and getting a 3 on at least one die.

I just really don\'t understand this concept or how you can derive this using the sum rule of probabality. The answer is 11/36.

Solution

There are 3 cases:

1. You a get a 3 on the first, and not a 3 on the second.

2. You don\'t get a 3 on the first, and get a 3 on the second.

3. You get both 3\'s.

Note that

P(3) = 1/3
P(not 3) = 5/6

Case 1:

P1 = (1/6)(5/6) = 5/36

Case 2:

P2 = (5/6)(1/6) = 5/36

Case 3:

P3 = (1/6)(1/6) = 1/36

Adding these three cases\' probabilities,

P(at least one three) = 5/36 + 5/36 + 1/36

= 11/36 [ANSWER]