Probability → Vocabulary → Formula → Example Questions → Addition of Probabilities

First consider what are joint (or not-mutually exclusive) and disjoint (or mutually exclusive) events.

Suppose, we have sample space

Then even and odd numbers in the above set are disjoint events. As Even Numbers = 2, 4,6 and Odd Numbers = 1, 3, 5

But, if we are interested in even numbers and multiples of three, then

Even Numbers = 2, 4, 6 and

Multiples of Three = 3, 6

So, 6 is a joint element.

**Addition Rule: Disjoint Events**

**Addition Rule: Joint Events**

**Remember:**

**Example 1.** A dice is rolled once. What is the probability that the number shown is 3 or even number?

Solution

3 is one event out of total 6 events, and even numbers {2,4,6} are three events out of total six events. Thus their probabilities are

, and

Thus,

**Example 2.** A dice is rolled once. What is the probability that the number shown is 3 or odd number?

**Solution**

, and

Now, there is one joint element i.e. 6. So,

Thus,