 # 7.3 Probability of Mutually Exclusive Events

7.3 Probability of Mutually Exclusive Events
1. Two events are mutually exclusive if they cannot occur at the same time.

2.
If A and B are mutually exclusive events, then

 P (A υ B) = P (A) + P (B)
Example:
A bag contains 3 blue cards, 4 green cards and 5 yellow cards. A card is chosen at random from the box. Find the probability that the chosen card is green or yellow.

Solution:
Let G = event when a green card is chosen.
= event when a yellow card is chosen.
The sample space, S = 12, (S) = 12
(G) = 4 and (Y) = 5

$\begin{array}{l}P\left(G\right)=\frac{n\left(G\right)}{n\left(S\right)}=\frac{4}{12}\\ P\left(Y\right)=\frac{n\left(Y\right)}{n\left(S\right)}=\frac{5}{12}\end{array}$

Events G and Y cannot occur simultaneously because we cannot obtain green card and yellow card at the same time. Therefore, events G and Y are mutually exclusive.

$\begin{array}{l}G\cap Y=\varnothing \\ P\left(G\cup Y\right)=\text{}P\left(G\right)+P\left(Y\right)\\ \text{}=\frac{4}{12}+\frac{5}{12}\\ \text{}=\frac{9}{12}=\frac{3}{4}\end{array}$