Last Saturday I bought six oranges from Epsom market, of decent size and priced at 6 for £1, a good deal less than we usually pay. A little mixed looking, but I thought worth a punt.
In the event, a very mixed bag, seemingly of various varieties, perhaps the sweepings from the floor of some orange warehouse, lurking somewhere on some industrial estate, lurking somewhere in the Home Counties. Two of the oranges were entirely satisfactory, good even, although in different ways, one was OK and three were thrown away. One black rotten at the navel end, one was bitter, perhaps an escaped marmalade orange (see reference 1) and one was old.
Given that I find it very hard to judge an orange from the outside and that the average customer is going to find a dud orange on his plate at breakfast time rather off-putting, what should the green grocer do?
Suppose he is the sort of green grocer that goes to market at Nine Elms every morning.
Suppose that on this morning he is looking to buy ten ten kilo boxes of oranges. What should he do to test their quality?
He could open up ten oranges, chosen at random, and then both inspect and sample the interior. A proceeding which might take a few minutes and which might, after a few weeks of this, make him very sick of the smell and taste of oranges. What if he has to do this with all the stuff that he buys? Swedes, for example?
What about his prior probalilities?
He might be experienced enough to be able to judge the interior of an orange by inspection, without having to taste. Plus, the way that an orange peels is usually informative - but a lot slower than just cutting the thing in half and getting at the interior that way.
He could trust the chap from whom he buys the oranges to have already done all this, and priced his oranges accordingly. Which he could then pass on in the same way. You get what you pay for, never mind the fact that you might be annoying, perhaps even losing, some of your regular customers, if you pass on duds, whatever the price.
And anyway, this only moves the problem along a bit. What is the wholesaler to do?
Maybe a successful wholesaler does enough oranges to be able to afford to go in for good quality quality control, up to supermarket standards, so that he can be sure that not only are his oranges good, but also that they are reliably good. He can then put his certifying paper seals on his oranges and sell them on in good faith.
And then there is the grower. What balance between costs, land, variety, quality and reliability does he strike? Should he swing with the fashions in these matters, or does he do better with a long game?
Question: write a two page essay on this problem from a statistical point of view. You should include in your essays any assumptions you might make about the probability distributions of oranges. You may assume that you are unlikely to get full marks if you make no such assumptions.
Reference 1: http://www.psmv2.blogspot.co.uk/2015/08/culinary-affairs.html.
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