Final answer:
The probability of both independent events A and B occurring together, given their individual probabilities of P(A) = 0.02 and P(B) = 0.45, is calculated as P(A AND B) = P(A) × P(B) = 0.009.
Step-by-step explanation:
For two independent events A and B, the product rule of probability states that the probability of both A and B occurring is given by multiplying their individual probabilities. If P(A) is the probability of event A occurring and P(B) is the probability of event B occurring, then the probability of both A and B occurring (denoted as P(A AND B)) is P(A) × P(B).
In this case, we have P(A) = 0.02 and P(B) = 0.45. To find P(A AND B), we multiply these probabilities:
P(A AND B) = P(A) × P(B) = 0.02 × 0.45 = 0.009.
Thus, the probability of both events A and B occurring together is 0.009.