I tried to solve this problem by finding the area of the rectangle and the area shared by both semicircle. My difficult is how to find the area of the created by the two semicircles. Is my approach wrong?
Two semicircles are inscribed in a rectangle as shown so their diameters are opposite sides of the rectangle. What is the probability that a point randomly selected inside the rectangle will also be inside both semicircles? Express your answer as a decimal rounded to the nearest hundredth.
Best Answer
This is my approach in an example. Take one of the circles to be $x^2+y^2=1$, and the other to be $x^2+(y-1)^2=1$. We are interested in the area where the two circles overlap. First you need to find their intersection points by setting the equations equal. Then, you can evaluate the integral: $\int Top circle -Bottomcircle$ $ dx $. This will give you the area. I'll end here since you seemed to have trouble with this bit. NOTE: These equations are just used as an example of how to calculate such an area