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A square dart board is placed in the fir...

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.

Text Solution

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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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