The conditional probability, P(E1 | E2), of a power failure (given that a flood occurs) is 0.9, and the conditional probability, P(E2 | E1), of a flood (given that a power failure occurs) is 0.2. If the joint probability, P(E1 and E2), of a power failure and a flood is 0.1, determine the marginal probabilities, P(E1) and P(E2).
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