Question

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $20,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $20,000 and $25,000.

Suppose you bid $21,000. What is the probability that your bid will be accepted?

Answer 1

The probability that your bid of $21,000 will be accepted is 20%, since this is the proportion of the possible range of bids ($20,000 to $25,000) that falls below your bid.

Step-by-step explanation:

To calculate the probability that your bid will be accepted when you bid $21,000, we need to consider the range of possible bids from the other competitor, which is from $20,000 to $25,000. Since the competitor's bid is uniformly distributed, this means that all bids within this range are equally likely.

Because any bid over $20,000 can win and your bid is $21,000, the losing range for the competitor's bid, where you would win, is from $20,000 to just under $21,000. The length of this range is $21,000 - $20,000 = $1,000. The entire possible range for the competitor's bid is $25,000 - $20,000 = $5,000.

The probability that the competitor's bid is less than your bid of $21,000 is therefore the length of the winning range ($1,000) divided by the entire range ($5,000), which yields a probability of $1,000 / $5,000 = 0.2 or 20%.