Final answer:
The probability of A given B is 0.20. The probability of the union of A and B is 0.50 - (0.20)(0.30), and the probability of the intersection of A and B is (0.20)(0.30).
Step-by-step explanation:
In this case, the events A and B are independent. Since they are independent, we can use the formula P(A|B) = P(A) to find the conditional probability of A given B. So, P(A|B) = P(A) = 0.20.
To find the probability of the union of A and B (AUB), we use the formula P(AUB) = P(A) + P(B) - P(A∩B). Since A and B are independent, P(A∩B) = P(A)P(B). Substituting the given values, we have P(AUB) = 0.20 + 0.30 - (0.20)(0.30).
To find the probability of the intersection of A and B (A∩B), we can again use the formula P(A∩B) = P(A)P(B). Substituting the given values, we have P(A∩B) = (0.20)(0.30).