Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$,  $ P ( B )=0.4$,  $P ( A \cap B )=0.8$

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$P ( A )=0.5$,  $P ( B )=0.4$,  $P (A \cup B)=0.8$

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.

Similar Questions

Two aeroplanes $I$ and $II$ bomb a target in succession. The probabilities of $l$ and $II$ scoring a hit correctlyare $0.3$ and $0.2,$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

  • [AIEEE 2007]

Fill in the blanks in following table :

$P(A)$ $P(B)$ $P(A \cap B)$ $P (A \cup B)$
$0.5$ $0.35$ .........  $0.7$

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