Check whether following probabilities P(A) and P(B) are consistently defined P ( A )=0.5 , P (

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14.Probability

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

Option A

Option B

Option C

Option D

Solution

$P ( A )=0.5$, $P ( B )=0.7$, $P (A \cap B)=0.6$

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.

Standard 11

Mathematics

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