Final answer:
To find the probability of the union of two events A and B, subtract the intersection of A and B from the sum of their individual probabilities. To find the conditional probability of A given B, divide the intersection of A and B by the probability of B.
Step-by-step explanation:
Given that events A and B are independent, we can find the probability of the intersection of A and B, denoted by A ∩ B, by multiplying the probabilities of A and B together. In this case, P(A∩B) = 0.15, which is the intersection of A and B.
To find the probability of the union of A and B, denoted by AUB, we can use the formula P(AUB) = P(A) + P(B) - P(A∩B). Substituting the given probabilities, we have P(AUB) = 0.20 + 0.30 - 0.15 = 0.35.
To find the conditional probability of A given B, denoted by P(A|B), we can use the formula P(A|B) = P(A∩B) / P(B). Since we know P(A∩B) = 0.15 and P(B) = 0.30, we have P(A|B) = 0.15 / 0.30 = 0.5.