Ononot — Let A and B be independent events with P(A) = 0.4 and P(B) =

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Probability Basicshard

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Let $A$ and $B$ be independent events with $P(A) = 0.4$ and $P(B) = 0.5$ . A third event $C$ has the following conditional probabilities:

$P(C \mid A \cap B) = 0.6$

$P(C \mid A^c \cap B) = 0.2$

$P(C \mid A \cap B^c) = 0.3$

$P(C \mid A^c \cap B^c) = 0.1$ Determine the conditional probability $P(A \cap B \mid C)$ .