Continuous Probability Problem

[Zraic]

Two insurers provide bids on an insurance policy to a large company. The bids must be between 2000 and 2200. The company decides to accept the lower bid if the two bids differ by 20 or more. otherwise, the company will consider the 20 bids further. Assume that the two bids are independent and are both uniformly distributed on the interval 2000 to 2200.

Determine the probability that the company considers the two bids further.

[Gandalf]

Draw the region (all possible pairs of bids) in the xy-plane. Shade the part of that region that corresponds to |x-y|<20. Since the density is uniform, the probability that they are within 20 is the ratio of the shaded area to the total area.

[chronoz5707]

I love uniform continuous problems in P, generally need to draw a region, then shade the required a region, take the proportion of the area of shaded area to the whole region. No messy integration involve.