Question 155575: In Indianapolis, the distance between the conference center and the airport is ten miles, and the distance between the conference center and my hotel is also ten miles.What is the probability that the hotel is closer to theairport than to the conferance center? Please Show all work.
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! The first thing I would do is draw a picture. Since the Hotel (H) and Airport (A) are each 10 miles from the Conference Center (CC), they are both on a circle of radius 10 centered at the Conference Center. So now look at the question. You want the distance between A and H to be less than the distance between CC and H. But we know the distance between CC and H is 10. So we want the probability that the distance between A and H is less than 10. Both A and H can be at any point on that circle's edge. The circumference of the circle is 2pi*radius, or 20pi miles. If you choose a place on that circle for H, A can be up to 10 miles to the left or 10 miles to the right to be closer than CC. So a total of 20 miles make A and H closer than A and C. The probability of A being within those 20 miles, rather than the rest of the circle, is 20/20pi, or 1/pi, or approximately 31.7%.
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