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statistics - conditional probability

Event A has probability 0.9 of occurring. Event B has 0.2 chance of occurring if, and only if, event A has occurred. What is the overall probability that event B will occur?

I'm so confused. This seems so simple, I'm not sure why I can't reason through it. They're not independent events...

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  1. 9. An event A will occur with probability 0.4. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.24. We may conclude

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