md65536 Posted June 22, 2012 Share Posted June 22, 2012 (edited) A farmer (on an island of course) has 100 cows in a barn. Each is brown or blue, and each was purchased from a supplier that randomly sells a brown or a blue cow with equal likelihood. The farmer tells a farmhand to go in and let a brown cow out. A brown cow is let out. What is the expected proportion of brown cows to total cows? Edited June 22, 2012 by md65536 Link to comment Share on other sites More sharing options...
Joatmon Posted June 22, 2012 Share Posted June 22, 2012 (edited) Sorry - changed my mind Edited June 22, 2012 by Joatmon Link to comment Share on other sites More sharing options...
J.C.MacSwell Posted October 17, 2012 Share Posted October 17, 2012 Still 50% is the most likely expectation Link to comment Share on other sites More sharing options...
md65536 Posted October 17, 2012 Author Share Posted October 17, 2012 Still 50% is the most likely expectation Unless I worded it wrong, the expected proportion will be the mean of all equally probable possible proportions. The mean can be fractional. You've given the mode. Link to comment Share on other sites More sharing options...
John Cuthber Posted October 17, 2012 Share Posted October 17, 2012 "What is the expected proportion of brown cows to total cows? " Where? Link to comment Share on other sites More sharing options...
EquisDeXD Posted October 17, 2012 Share Posted October 17, 2012 Same answer as the one I posted in the other one? Link to comment Share on other sites More sharing options...
J.C.MacSwell Posted October 18, 2012 Share Posted October 18, 2012 Unless I worded it wrong, the expected proportion will be the mean of all equally probable possible proportions. The mean can be fractional. You've given the mode. You can't expect the actual result to be. (I'm just throwing out my $.02, even if it might be overpriced, and taking "expected proportion" somewhat literally, as "most expected proportion") Does "expected proportion" have a defined meaning in statistics? (not my field) I don't assume it has one in brain teasers. Link to comment Share on other sites More sharing options...
md65536 Posted October 18, 2012 Author Share Posted October 18, 2012 You can't expect the actual result to be. (I'm just throwing out my $.02, even if it might be overpriced, and taking "expected proportion" somewhat literally, as "most expected proportion") Does "expected proportion" have a defined meaning in statistics? (not my field) I don't assume it has one in brain teasers. Not my field either, and I'm in over my head now. I didn't mean for this to be a brain teaser or trick, just a quick stats puzzle. As mentioned by someone in a similar thread, these puzzles assume a Bayesian interpretation of probability, where it's possible to reason about an uncertain count of brown cows. So the expected count expresses probability, and can be fractional until enough information is known to make the count certain, in which case it would be integral. I meant for the expected proportion to represent the uncertain proportion, given only what information is in the puzzle. Sorry about the ambiguity! Link to comment Share on other sites More sharing options...
John Cuthber Posted October 18, 2012 Share Posted October 18, 2012 Rather than being sorry about the ambiguity, try clearing it up. Answer my earlier question. When you say "What is the expected proportion of brown cows to total cows?" which cows are you referring to? All cows on the island, those in the barn or those outside the barn? Also, cows are not blue unless you paint them. If the vendor supplies blue cows it's possible that the paint washes off in the rain. After a while all cows will be brown (or white or whatever). Is it reasonable to assume that cows do not change colour? "During your daily contact with your cattle, always be on the lookout for any physical or behavioral changes. Symptoms indicating illness include listlessness, pale coloring, limping, loss of appetite, teeth grinding, coughing, and abnormal temperature" from http://www.farmsanctuary.org/wp-content/uploads/2012/06/Animal-Care-Cattle.pdf Link to comment Share on other sites More sharing options...
EquisDeXD Posted October 18, 2012 Share Posted October 18, 2012 Yeah if my answer isn't in any way correct, and the cows were painted blue, then the paint could have worn off before you asked the question, making it 100% brown cows, or it could be 0% because someone painted all the brown cows blue. Link to comment Share on other sites More sharing options...
md65536 Posted October 19, 2012 Author Share Posted October 19, 2012 Rather than being sorry about the ambiguity, try clearing it up. Answer my earlier question. When you say "What is the expected proportion of brown cows to total cows?" which cows are you referring to? The 100 cows specifically mentioned in the puzzle. Where they are is irrelevant. The only point in mentioning the barn is to justify the reasoning that you don't have any further info about the cows because they're hidden. This isn't a trick question. Yeah if my answer isn't in any way correct, and the cows were painted blue, then the paint could have worn off before you asked the question, making it 100% brown cows, or it could be 0% because someone painted all the brown cows blue. This is just a stats puzzle, not a lateral-thinking puzzle. The puzzle implies the existence of blue cows. That can be assumed. Link to comment Share on other sites More sharing options...
John Cuthber Posted October 19, 2012 Share Posted October 19, 2012 Is the answer you are looking for (1+ 99/2) /100 ? Link to comment Share on other sites More sharing options...
md65536 Posted October 19, 2012 Author Share Posted October 19, 2012 Is the answer you are looking for (1+ 99/2) /100 ? No. The other 99 cows are not equally likely to be brown or blue. Link to comment Share on other sites More sharing options...
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