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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Here are two variations of the Monty Hall problem that are discussed by Granberg.<ref group="Notes" >D. Granberg, “To switch or not to switch,” in ''The power of logical thinking,'' M. vos~Savant, (New York: St.\ Martin's 1996).</ref> <ul><li...") |
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Here are two variations of the Monty Hall problem that are discussed by Granberg.<ref group="Notes" >D. | Here are two variations of the Monty Hall problem that are discussed by Granberg.<ref group="Notes" >D. | ||
Granberg, “To switch or not to switch,” in | Granberg, “To switch or not to switch,” in | ||
''The power of logical thinking,'' M. vos | ''The power of logical thinking,'' M. vos Savant, (New York: St.\ Martin's | ||
1996).</ref> | 1996).</ref> | ||
<ul><li> | <ul style="list-style-type:lower-alpha"><li> | ||
Suppose that everything is the same except that Monty forgot to find out in advance which door has the car behind | Suppose that everything is the same except that Monty forgot to find out in advance which door has the car behind | ||
it. In the spirit of “the show must go on,” he makes a guess at which of the two doors to open and | it. In the spirit of “the show must go on,” he makes a guess at which of the two doors to open and | ||
| Line 16: | Line 9: | ||
</li> | </li> | ||
<li> | <li> | ||
You have observed the show for a long time and found that the car is put behind door A 45 | You have observed the show for a long time and found that the car is put behind door A 45% of the time, | ||
behind door B 40 | behind door B 40% of the time and behind door C 15% of the time. Assume that everything else | ||
about the show is the same. Again you pick door A. Monty opens a door with a goat and | about the show is the same. Again you pick door A. Monty opens a door with a goat and | ||
offers to let you switch. Should you? Suppose you knew in advance that Monty was going to give you | offers to let you switch. Should you? Suppose you knew in advance that Monty was going to give you | ||
Latest revision as of 00:23, 13 June 2024
Here are two variations of the Monty Hall problem that are discussed by Granberg.[Notes 1]
- Suppose that everything is the same except that Monty forgot to find out in advance which door has the car behind it. In the spirit of “the show must go on,” he makes a guess at which of the two doors to open and gets lucky, opening a door behind which stands a goat. Now should the contestant switch?
- You have observed the show for a long time and found that the car is put behind door A 45% of the time, behind door B 40% of the time and behind door C 15% of the time. Assume that everything else about the show is the same. Again you pick door A. Monty opens a door with a goat and offers to let you switch. Should you? Suppose you knew in advance that Monty was going to give you a chance to switch. Should you have initially chosen door A?
Notes