[tex]$A$[/tex] and [tex]$B$[/tex] are mutually exclusive events. [tex]$P(A) = 0.60$[/tex] and [tex]$P(B) = 0.20$[/tex]. What is [tex]$P(A \text{ or } B)$[/tex]?

A. 0.80
B. 0.68
C. 0.12
D. 0.40



Answer :

To find the probability of either event [tex]\( A \)[/tex] or event [tex]\( B \)[/tex] happening, denoted as [tex]\( P(A \cup B) \)[/tex], we use the fact that [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are mutually exclusive events. This means that they cannot both occur at the same time, or in other words, the joint probability of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] occurring together, [tex]\( P(A \cap B) \)[/tex], is zero.

The formula for the probability of the union of two events is:

[tex]\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \][/tex]

Since [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are mutually exclusive, [tex]\( P(A \cap B) = 0 \)[/tex]. Therefore, the formula simplifies to:

[tex]\[ P(A \cup B) = P(A) + P(B) \][/tex]

Given in the problem:

- [tex]\( P(A) = 0.60 \)[/tex]
- [tex]\( P(B) = 0.20 \)[/tex]

We substitute these values into the simplified formula:

[tex]\[ P(A \cup B) = 0.60 + 0.20 \][/tex]

[tex]\[ P(A \cup B) = 0.80 \][/tex]

Thus, the probability of either event [tex]\( A \)[/tex] or event [tex]\( B \)[/tex] happening is [tex]\( 0.80 \)[/tex].

So, the correct answer is [tex]\( \boxed{0.80} \)[/tex].