Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$, $ P ( B )=0.7$, $P ( A \cap B )=0.6$
Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$, $ P ( B )=0.7$, $P ( A \cap B )=0.6$
$P ( A )=0.5$, $P ( B )=0.7$, $P (A \cap B)=0.6$
It is known that if $E$ and $F$ are two events such that $E \subset F,$ then $P ( E ) \leq P ( F )$
However, $P (A \cap B)> P ( A )$
Hence, $P ( A )$ and $P ( B )$ are not consistently defined.
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- [IIT 2002]
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