King Midas suspected that his minter of gold coins, Horatio, was stealing from the mint by inserting false coins.<\/p>\n
As he had 1000 boxes, each containing 100 coins, ready for shipment to King Neptune to pay for construction of some luxury ships, he wondered how he best could check on his suspicions.<\/p>\n
So he called on the court mathematician, Leonard, for advice.<\/p>\n
\u201cI want to make 99% sure that there is a maximum of 1% of counterfeit coins in the shipment. How can this be done,\u201d he demanded of Leonard.<\/p>\n
\u201cSire, I can have a number of the boxes checked, selecting a sample of one coin at random until we find a false coin,\u201d said Leonard.<\/p>\n
\u201cHow many boxes will have to be checked,\u201d asked King Midas.<\/p>\n
\u201cIt depends on the percentage of false coins in them,\u201d replied Leonard. \u201cI will give you a number of boxes to be checked for the case of 1% false coins and a number for 10% false coins.”<\/p>\n
After some thought, Leonard gave King Midas the respective number of boxes.<\/p>\n
\u201cVery well, proceed. If Horatio has been greedy, he will very quickly lose his head,\u201d thundered King Midas.<\/p>\n
How many boxes would have to be checked to ensure that 99% of the shipment had less than one false coin per hundred coins?<\/em><\/p>\n If there actually were 10% of false coins, after how many random boxes checked on the average would this be discovered?<\/em><\/p>\nShare this:<\/h3>