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counting and probability intermediate

Problem

If two lines and have equations , and , what is the probability that a point randomly selected in the 1st quadrant and below will fall between and ? Express your answer as a decimal to the nearest hundredth.

problem
Solution
We first find the areas of the triangles under and and in the first quadrant. From 's equation, we find that at , . From , we find that at , we find that .

We then find the areas using the formula for a triangle: . The area under is . The area under is . Thus, the probability that the point selected will fall between and has probability . Thus, the probability is .
Final answer
0.75