Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$, $ P ( B )=0.4$, $P ( A \cap B )=0.8$
Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$, $ P ( B )=0.4$, $P ( A \cap B )=0.8$
$P ( A )=0.5$, $P ( B )=0.4$, $P (A \cup B)=0.8$
It is known that if $E$ and $F$ are two events such that $E \subset F,$ then $P ( E ) \leq P ( F )$
Here, it is seen that $P (A \cup B)> P ( A )$ and $P (A \cup B)> P ( B )$
Hence, $P(A)$ and $P(B)$ are consistently defined.
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- [IIT 1994]
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