Statement-1: \[\frac{4}{15}\le P(A\cap B)\le \frac{3}{5}.\] |
Statement-2: \[\frac{2}{5}\le P\left( \frac{A}{B} \right)\le \frac{9}{10}\] |
A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
C) Statement-1 is true, Statement-2 is false.
D) Statement-1 is false, Statement-2 is true.
Correct Answer: B
Solution :
\[\because \] \[(A\cup B)\ge P(A)+P(B)-1\] \[\therefore \]\[P(A\cap B)=\frac{3}{5}+\frac{2}{3}-1\Rightarrow P(A\cap B)\ge \frac{4}{15}\]?(i) \[\because \]\[P(A\cap B)\le P(A)\Rightarrow P(A\cap B)\le \frac{3}{5}\] From (i) and (ii), \[\frac{4}{15}\le P(A\cap B)\le \frac{3}{5}\] ...(iii) From (iii), \[\frac{4}{15P(B)}\le \frac{P(A\cap B)}{P(B)}\le \frac{3}{5P(B)}\]\[\Rightarrow \]\[\frac{2}{5}\le P\left( \frac{A}{B} \right)\le \frac{9}{10}\]You need to login to perform this action.
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