Question

If a point $A(x, y)$ lies in the region bounded by the $y$-axis, straight lines $2y + x = 6$ and $5x – 6y = 30$, 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)

$\frac{5}{6}$

Answer 2

The required probability

= $\frac{\text{Area of Region PQCAP}}{\text{Area of Region ABCA}}$

=$\frac{\frac{1}{2}×8×6−\frac{1}{2}×2×4}{\frac{1}{2}×8×6}$

$= \frac{5}{6}$

So, Correct option is (B): $\frac{5}{6}$