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Intersection of Sets

Check whether...

Question

Check whether the probabilities $P (A)$ and $P (B)$ are consistently defined
$P (A) = 0.5, P (B) = 0.7, P (A \cap B) = 0.6$

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Solution

$P (A) = 0.5$

$P (B) = 0.7$

$P (A \cap B) = 0.6$

Since $P (A \cap B) > P (A)$

Thus its not consistent

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