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

Vedclass pdf generator app on play store
Vedclass iOS app on app store

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

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.

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]

Given two independent events $A$ and $B$ such that $P(A) $ $=0.3, \,P(B)=0.6$ Find $P(A$ and $B)$.

Fill in the blanks in following table :

$P(A)$ $P(B)$ $P(A \cap B)$ $P (A \cup B)$
$\frac {1}{3}$ $\frac {1}{5}$ $\frac {1}{15}$  ........

For any two events $A$ and $B$ in a sample space

  • [IIT 1991]

$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P \left( B \cap A ^{\prime}\right)$.