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# Using Geometry in Probability!

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If two lines \$l\$ and \$m\$ have equations \$y = -x + 6\$, and \$y = -4x + 6\$, what is the probability that a point randomly selected in the 1st quadrant and below \$l\$ will fall between \$l\$ and \$m\$? Express your answer as a decimal to the nearest hundredth.

Mar 29, 2018

### 1+0 Answers

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The area  below l  and still in the first quadrant  is a triangle with a base of 6 and a height of 6

So...its area  is    base * height /2  =  6 * 6 /2  =   18 units^2   (1)

The area between the two lines also forms a triangle with a height of 6  and a base of 4.5

So...its area   is   6 * 4.5  / 2  =  13.5  units^2    (2)

So...the probability of a point being selected in the specified area  is   (2)  / (1)  =

13.5  / 18   = 0.75   Mar 29, 2018