The “Match-Made-In-Heaven” internet dating service charges $20 per date that it

Question

The “Match-Made-In-Heaven” internet dating service charges $20 per date that it arranges. All of their dates will accept an offer of marriage, even if you date others from the site later. In your opinion, the quality of the potential spouses offered by the dating service can be measured by an index that runs from 0 to 10 cows. The potential spouses are uniformly distributed over this range. Suppose the price of cattle is $100 each. If your dates were drawn at random from the pool of potential dates, at what cow-value should you stop searching? (Clarifying point: the cattle do not have to be paid once you have decided to marry the spouse, so if you get a 10-cow spouse, you get $1000 of benefit)

Explanation / Answer

Let us look this case wise. If a spouse is randomly selected, the probability that it will be a 0 cow index spouse is equal to that of 10 cw indexed spouse, and its true for any other index in between. Now suppose, a 0 cow index spouse is arranged. In this case, we get a benefit of $ 0 while, we are to pay $ 20; thus on total we incurred a loss of $ 20. Now if 1 cow indexed spouse turns up then, we reap a benefit of $ 100 while we are paying only $ 20. Thus we are making a profit in transaction. The same would be true for all other higher indexed cows. Hence, financially one can stop if he/she gets 1 cow indexed spouse.

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