To find the probability of two independent events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring together, we use the formula:
[tex]\[ P(A \text{ and } B) = P(A) \times P(B) \][/tex]
We know from the problem statement that:
[tex]\[ P(A) = 0.50 \][/tex]
[tex]\[ P(B) = 0.20 \][/tex]
Now, we need to multiply these probabilities together:
[tex]\[
P(A \text{ and } B) = 0.50 \times 0.20
\][/tex]
By performing the multiplication, we get:
[tex]\[
P(A \text{ and } B) = 0.10
\][/tex]
So, the probability of both [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring together is:
[tex]\[
P(A \text{ and } B) = 0.10
\][/tex]
Thus, the correct answer is:
D. 0.10
