A) \[\frac{7}{16}\]
B) \[\frac{3}{4}\]
C) \[\frac{7}{12}\]
D) \[\frac{21}{64}\]
Correct Answer: C
Solution :
\[\because \] \[f(x)=\frac{x}{2}\] \[(0\le x\le 2)\] Now, \[P(x>1.5)=\int_{1.5}^{2}{\frac{x}{2}dx}\] \[=0.4375\] and \[P(x>1)=\int_{1}^{2}{\frac{x}{2}dx}=0.75\] Hence, \[P\left( \frac{X>1.5}{X>1} \right)=\frac{P(X>1.5)}{P(X>1)}\] \[=\frac{0.4375}{0.75}=\frac{7}{12}\]
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