Two insurers provide bids on an insurance policy to a large company. The bids are 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 two bids further. Assume that the two bids are independent and are both uniformly distributed on the interval from $2000 to $2200. (a) Run a Monte Carlo simulation to estimate the probability that the company considers the two bids further.
(b) Assume that one of the insurers provided a bid of $2,100 (and you don't know the bid provided by the other). Compute the probability that the company will accept one of the bids. You are expected to provide an exact mathematical derivation here, not a Monte Carlo approximation.