If a point A(x, y) lies in the region bounded | vedclass

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(B) The region is bounded by the $y$-axis $(x=0)$,$2y+x=6$,and $5x-6y=30$. The vertices of the triangle are $B(0, 3)$,$C(0, -5)$,and $A(6, 0)$.Area of

Vedclass · Accepted Answer

$\frac{5}{6}$

Vedclass · Answer

(B) The region is bounded by the $y$-axis $(x=0)$,$2y+x=6$,and $5x-6y=30$. The vertices of the triangle are $B(0, 3)$,$C(0, -5)$,and $A(6, 0)$.Area of $	riangle ABC = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 8 	imes 6 = 24$.The line $y=1$ intersects $2y+x=6$ at $D(4, 1)$ and the $y$-axis at $E(0, 1)$.The region where $y The area of $	riangle BDE$ (where $y \ge 1$) is $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 4 	imes 2 = 4$.Required probability $= 1 - \frac{	ext{Area}(	riangle BDE)}{	ext{Area}(	riangle ABC)} = 1 - \frac{4}{24} = 1 - \frac{1}{6} = \frac{5}{6}$.

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

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