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# True-or-False : If A and B are two candidates seeking admission in an engineering college.The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3.Is it possible that the probability of B getting selected is 0.7?

$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array}$

Can you answer this question?

Toolbox:
• $P(A \cup B)=P(A)+P(B)-P(A \cap B)$
Given :
$P(A)=0.5$
$P(A\cup B)=0.3$
$P(B)=0.7$
$\therefore$ If $P(B)=0.7$
Then $P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$0.3=0.5+0.7-P(A \cap B)$
$\Rightarrow P(A \cap B)=0.9$
$\therefore$ It satisfies the statement and the statement is True.
answered Jul 9, 2014