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17 Aug 2005 - 21:29
low birth weight paradox (& Monty Hall)
Monty Hall, part 2
false positives
false positives, part 2
Doug Sundseth on Monty Hall
John Kay: We are likely to get probability wrong (subscription only)
Monty Hall diagram from Curious Incident
probability question from Saxon 8/7
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It took me a long time to understand it, too. The model that finally worked for me was something like this: You have a 1/3 chance of being right to start with, and a 2/3 chance of being wrong. If you guessed wrong originally, Monte's pick will unambiguously determine the correct choice (he never picks the good door). There are nine pairs of (your pick):(correct pick), A:A, A:B, A:C, B:A, B:B, B:C, C:A, C:B, and C:C. In three of those, you picked correctly, Monte's information isn't useful, and you shouldn't switch. In the other six, you picked incorrectly and Monte told you which of the other picks was correct; thus you should switch. If you never switch, you have three chances in nine of being correct. If you always switch, you have six chances in nine of being correct and three chances in nine of switching off the correct choice. Note that the latter possibility (choosing correctly at random then switching to an incorrect choice) may be more psychologically painful than just guessing wrong and not switching. This may have an undue effect on the choices of contestants. -- DougSundseth - 17 Aug 2005
Monty Hall, part 2
Here is Kay on the Monty Hall problem:The Monty Hall problem is named after the host of a 1970s quiz show, Let’s Make a Deal. The successful contestant chooses from three closed boxes. One contains the keys to a car and the other two a picture of a goat. The choice made, Monty opens one of the other doors to reveal – a goat. He taunts the guest to change the decision. Should the guest switch to the other closed box? When the solution was published in an American magazine, thousands of readers – including professors of statistics – alleged an error. Paul Erdös, the great mathematician, reputedly died still musing on the Monty Hall problem. But the answer is, indeed, yes: you should change.I'm happy to hear that Paul Erdos stumbled over Monty Hall, seeing as how I still don't understand it.
low birth weight paradox (& Monty Hall)
Monty Hall, part 2
false positives
false positives, part 2
Doug Sundseth on Monty Hall
John Kay: We are likely to get probability wrong (subscription only)
Monty Hall diagram from Curious Incident
probability question from Saxon 8/7
Back to main page.
Comments
After entering a comment, users can login anonymously as KtmGuest (password: guest) when prompted.Please consider registering as a regular user.
Look here for syntax help.
It took me a long time to understand it, too. The model that finally worked for me was something like this: You have a 1/3 chance of being right to start with, and a 2/3 chance of being wrong. If you guessed wrong originally, Monte's pick will unambiguously determine the correct choice (he never picks the good door). There are nine pairs of (your pick):(correct pick), A:A, A:B, A:C, B:A, B:B, B:C, C:A, C:B, and C:C. In three of those, you picked correctly, Monte's information isn't useful, and you shouldn't switch. In the other six, you picked incorrectly and Monte told you which of the other picks was correct; thus you should switch. If you never switch, you have three chances in nine of being correct. If you always switch, you have six chances in nine of being correct and three chances in nine of switching off the correct choice. Note that the latter possibility (choosing correctly at random then switching to an incorrect choice) may be more psychologically painful than just guessing wrong and not switching. This may have an undue effect on the choices of contestants. -- DougSundseth - 17 Aug 2005
| WebLogForm | |
|---|---|
| Title: | Monty Hall, part 2 |
| TopicType: | WebLog |
| SubjectArea: | FractionsDecimalsAndPercents, MathProblemHelpLine, StatisticsAbuse, StatisticsTeaching |
| LogDate: | 200508171728 |