To solve the problem of finding the probability of both events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring, given that [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are independent events, we need to use the multiplication rule for independent events.
The multiplication rule for independent events states that if [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are independent, then the probability of both [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring is given by the product of their individual probabilities:
[tex]\[ P(A \text{ and } B) = P(A) \times P(B) \][/tex]
We are given:
[tex]\[ P(A) = 0.80 \][/tex]
[tex]\[ P(B) = 0.10 \][/tex]
Substitute the given probabilities into the multiplication rule:
[tex]\[ P(A \text{ and } B) = 0.80 \times 0.10 \][/tex]
Perform the multiplication:
[tex]\[ P(A \text{ and } B) = 0.08 \][/tex]
Thus, the probability of both [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring is [tex]\(0.08\)[/tex].
The correct answer is:
B. 0.08
