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

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.

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)

390
/
27000

= 0.014

P (male) =

15000
/
27000

= 0.555

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)