A and [tex]$B$[/tex] are independent events. [tex]$P(A)=0.40$[/tex] and [tex]$P(B)=0.20$[/tex]. What is [tex]$P(A$[/tex] and [tex]$B)$[/tex]?

A. 0.80
B. 0
C. 0.60
D. 0.08



Answer :

To determine the probability of both events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring together, denoted as [tex]\(P(A \text{ and } B)\)[/tex], we use the property of independent events. When two events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are independent, the probability of both events happening simultaneously is the product of the probabilities of each event occurring individually.

Given:
- [tex]\(P(A) = 0.40\)[/tex]
- [tex]\(P(B) = 0.20\)[/tex]

The formula for the probability of both independent events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring is:

[tex]\[ P(A \text{ and } B) = P(A) \times P(B) \][/tex]

Substituting the given values:

[tex]\[ P(A \text{ and } B) = 0.40 \times 0.20 \][/tex]

Perform the multiplication:

[tex]\[ 0.40 \times 0.20 = 0.08000000000000002 \][/tex]

Thus, the probability of both events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring together is [tex]\(0.08\)[/tex].

The correct answer is:

D. 0.08