Monty hall problemo

[Luke]

hey. so i was stuck on a multiple choice question during an afrikaans exam yesterday and i had absolutely no idea about the answer so i employed the monty hall game show logic to help me get the answer.

 

there were four possible answers: A B C D

so i wrote down each letter on an equally sized piece of paper, shuffeled the papers around in my hands a bit and took an answr out at random. this answer had a 3 in 4 chance of being the incorrect answer (75%) sure that the answer was wrong. now i three answers left. i shuffled them and took another at ranom. this one had a 66.6% chance of being incorrect. so now i was left with two possible answers that should statistically have a higher chance of being correct, compared to the other two answers that were drawn out first. so now i just had to take a guess between the last two which were answer A and B.

 

now my question is: chances were that the two first drawn answers were incorrect ( which were C and D), but now why would it be incorrect to assume that in any multiple choice question with four possible answers that answers C and D are incorrect?

[lawcat]

chances were that the two first drawn answers were incorrect ( which were C and D),

 

That's right. Chances were 75% that each was incorrect. That chance is based on science of statistics.

but now why would it be incorrect to assume that in any multiple choice question with four possible answers that answers C and D are incorrect?

 

But then, you took a leap of faith and departed from statistics. You presumed that because D has a 75% statistical chance that, then it has 100% chance. But 75 =/= 100. You discarded D. You were left with 3 choices. Now you said, C has 66% chance. Then you discraded C becuase if C has 66% then it has 100% chance of being incorrect. But 66 =/=100.

 

That's not statistics. That's fuzzy math :rolleyes:

 

Good luck in your gambling adventures.

[Qfwfq]

This is not how the Monty Hall problem works, at all.

 

MH disclosed one of the unchosen options, presumably knowing that it wouldn't turn out to be winning. The difference in probability is between the contestant's first choice --still unknown-- and the remaining other options. My explanation for the counter-intuitive effect is that the contestant is partly exploiting Monty's knowledge of which box he should not have opened (assuming of course that he did know).