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If $$P(E \cap F) = 0.054$$ $$P(E |F) = 0.12$$ $$P(F | E) = 0.3$$

How Do I find P(F) or P(E)?

These are dependent of each other, so I was trying to use the fact that

$$P(E \cap F) = P(E |F)P(F)$$

By using this, I could isolate P(F) but that is not working. Could someone give me a hint?

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1 Answer

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We have that $$P(E\mid F)=\frac{P(E\cap F)}{P(F)}$$ and $$P(F\mid E)=\frac{P(E\cap F)}{P(E)}.$$ Hence, $$P(F)=\frac{P(E\cap F)}{P(E\mid F)}$$ and $$P(E)=\frac{P(E\cap F)}{P(F\mid E)}.$$

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