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
