The $Area$ inside $ADBC$ satisfies the $x^{2}+y^{2}\leq1$
The line $AB$ has $eq^{n}\,x+y=1$, the arrow represents the points which statisfy $x+y\leq1$
The $coloured\,region$ shows the area from where any point can be picked from the entire disk $ADBC$
$Area\, of\, the\, disk=\pi*1^{2}=\pi$
$Area\,of\,the\,coloured\,region=Area(ADCBO)+Area(AOB)$
$Area(ADCBO)=\frac{3}{4}*Area\,of\,disk=\frac{3}{4}*\pi$
$Area(AOB)=\frac{1}{2}*AO*OB=\frac{1}{2}*1*1=\frac{1}{2}$
$Area\,of\,the\,coloured\,region=\frac{3}{4}*\pi+\frac{1}{2}$
$Required\,Proabability=\frac{coloured\,region}{total\,area\,of\,disk}=\frac{\frac{3}{4}*\pi+\frac{1}{2}}{\pi}=\frac{3}{4}+\frac{1}{2}.\frac{1}{\pi}$
So, $(c)$ should be correct. Correct me If I'm wrong