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I am working with a problem that uses Bayes Theorem and conditional probabilities. I have the conditional probability that a plane has an emergency locator $(E)$ given that it was discovered $(D)$ which is $P(E\mid D)=0.60$. Now I am given that $P(E'\mid D')=0.90$, where a plane does not have a emergency locator given that it was not discovered. I wanted to know what the complement of $P(E'\mid D')$ would be. Is it $P(E\mid D)$ or $P(E\mid D')$? I am not sure whether or not to flip the $D$ in the conditional.

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2 Answers

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$$P(E\mid D')=1-P(E'\mid D')$$ and $$P(E'\mid D)=1-P(E\mid D)$$ if that is what you mean by complement

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It will be $P(E\mid D')$ irrespective of whether or not to flip the $D$ in the conditional.

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