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

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) (1/6) (B) (5/6) (C) (2/3) (D) (6/7)

Tardigrade Admin · Accepted Answer

Required probability =( textar( ADEC )/ textar( ABC )) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/ca343255e85c06455b6c39ab2616c321-.png" /> =1-( textar( BDE )/ textar( ABC )) =1-((1/2) × 2 × 4/(1)2 × 8 × 6)=1-(1/6)=(5/6)

Q. 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 :

$\frac{1}{6}$

$\frac{5}{6}$

$\frac{2}{3}$

$\frac{6}{7}$

Required probability $= \frac{ar ( A D EC )}{ar ( A BC )}$

$= 1 - \frac{ar ( B D E )}{ar ( A BC )}$
$= 1 - \frac{\frac{1}{2} \times 2 \times 4}{\frac{1}{2} \times 8 \times 6} = 1 - \frac{1}{6} = \frac{5}{6}$

Q. 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 :

61​

65​

32​

76​