Question

If a point $A ( x , y )$ lies in the region bounded by the $y$-axis, straight lines $2 y + x =6$ and $5 x -6 y =30$, then the probability that $y <1$ is :

• A. $\frac{1}{6}$
• B. $\frac{5}{6}$
• C. $\frac{2}{3}$
• D. $\frac{6}{7}$

Answer 1

Answer: (B)

Required probability $=\frac{\text{ar}( ADEC )}{\text{ar}( ABC )}$

$=1-\frac{\text{ar}( BDE )}{\text{ar}( ABC )}$
$=1-\frac{\frac{1}{2} \times 2 \times 4}{\frac{1}{2} \times 8 \times 6}=1-\frac{1}{6}=\frac{5}{6}$