Certainly! Let's solve this step-by-step.
Given:
- [tex]\( P(A) = 0.40 \)[/tex]
- [tex]\( P(B) = 0.20 \)[/tex]
- Events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are independent.
We need to find [tex]\( P(A \text{ and } B) \)[/tex].
Since events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are independent, the probability of both events occurring together, [tex]\( P(A \text{ and } B) \)[/tex], is given by the product of their individual probabilities:
[tex]\[ P(A \text{ and } B) = P(A) \times P(B) \][/tex]
Substituting the given probabilities:
[tex]\[ P(A \text{ and } B) = 0.40 \times 0.20 \][/tex]
This simplifies to:
[tex]\[ P(A \text{ and } B) = 0.08 \][/tex]
Therefore, the correct answer is:
D. 0.08
