Use of **Addition rule** for probability we show you how to find the probability of the union of two events.

We use the following table about gifted and untalented students.

What is the likelihood that a randomly selected student will be gifted or male?

First of all, we need to know how many students are gifted or male. Let G = gifted and M = male

The number of gifted or male students is the union of G and M, written as

G ∪ M

or

G or M

G ∪ M means either gifted or male or both.

To find G ∪ M, we need to add the number of gifted students to the number of male students.

Gifted = 150 + 240

Men = 150 + 14850

Gifted + men = 150 + 240 + 150 + 14850

Note, however, that 150 is counted twice. To avoid double counting we need to 150 out of 150 + 240 + 150 + 14850. subtract

150 is the number of students who are gifted and male at the same time, or G ∩ M

If you don’t subtract 150, you will count G ∩ M twice

The number of talented or male students is

GM = 150 + 240 + 150 + 14850 – 150 = 15240.

Let G ∪ M be the probability that a student is gifted or male.

P (G ∪ M) =

15240

27000

= 0.564

G ∪ M = G + M – G ∩ M

Let us calculate for the following probability

P (GM) = P (G) + P (M) – P (G ∩ M)

P (gifted) =

390

27000

= 0.014

P (male) =

15000

27000

= 0.555

P (gifted ∩ male) =

150

27000

= 0.005

P (G ∪ M) = 0.014 + 0.555 – 0.005 = 0.569 – 0.005 = 0.564

In general, the addition rule for the probability applies here.

Let A and B be two events.

Then P (A or B) = P (A) + P (B) – P (A and B)

## Addition rule for the probability when the events are mutually exclusive

If A and B are mutually exclusive, it means that A ∩ B = {}

So P (A and B) = 0

P (A or B) = P (A) + P (B)