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A square dart board is placed in the first quadrant from x = 0 to x = 6 and y = 0 to y = 6. A triangular region on the dart board is enclosed by y = 2

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A square dart board is placed in the first quadrant from x = 0 to x = 6 and y = 0 to y = 6. A triangular region on the dart board is enclosed by y = 2, x = 6 and y = x. Find the probability that a dart that randomly hits the dart board will land in the triangular region formed by the three lines. Select the correct answer from above options

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Area of square board `=(6)^(2)=36` sq. units `"Now, "DE= 6-2=4 units` BD = 6-2=4 uints `therefore" Area of "triangleBDE=(1)/(2)xxDExxBD=(1)/(2)xx4xx4` = 8 sq. units `" Hence, required probability "=("Area of "triangleBDE)/("Area of square OABC")` `=(8)/(6xx6)=(2)/(9)`

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