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:

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$\frac{1}{6}$

$\frac{5}{6}$

$\frac{2}{3}$

$\frac{6}{7}$

answer is B.

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Detailed Solution

The required probability

$= \frac{Area of Region P Q C A P}{Area of Region A B C A}$
$= \frac{\frac{1}{2} \times 8 \times 6 - \frac{1}{2} \times 2 \times 4}{\frac{1}{2} \times 8 \times 6}$
$= \frac{5}{6}$

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