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

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 &#60; 1 is

Aicharya · Accepted Answer

Plotting the diagram of the given straight line we get,

Now by diagram, required probability $= \frac{ar (A D E C)}{ar (A B C)}$

$= 1 - \frac{ar (B D E)}{ar (A B C)}$

$= 1 - \frac{\frac{1}{2} \times 2 \times 4}{\frac{1}{2} \times 8 \times 6} = 1 - \frac{1}{6} = \frac{5}{6}$

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 …