Addition theorem of two events:

If A and B are two events associated with a random experiment, then

P(A U B) = P(A) + P(B) - P(A ∩ B)

Again, 

If A and B are two mutually exclusive events, then P(A ∩ B) = 0

So, P(A U B) = P(A) + P(B)

Let us take some examples.

Example 1: What is the probability of getting a 2 or a 5 when a die is rolled?

Solution:

Probability of getting a 2 = 1/6

Probability of getting a 5 = 1/6

Probability of getting a 2 and 5 = 0

Now, Probability of getting a 2 or a 5,

P(2 or 5) = P(2) + P(5) – P(2 and 5)

              = 1/6 + 1/6 – 0

              = 2/6

              = 1/3

Example 2: Consider the example of finding the probability of selecting a black

card or a 6

from a deck of 52 cards.

Solution:

We need to find out P(B or 6)

Probability of selecting a black card = 26/52

Probability of selecting a 6 = 4/52

Probability of selecting both a black card and a 6 = 2/52

P(B or 6) = P(B) + P(6) – P(B and 6)

              = 26/52 + 4/52 – 2/52

              = 28/52

              = 7/13

In this way, we solve probability sum of given events.