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April 16th, 2013, 07:09 PM   #1
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Probability Question

Please help me understand probability. I have a couple of questions that are based on a game show involving 50 suitcases.

Question 1. 50 suitcases, one has money in it, you get to pick one. It has a 2% probability of being the one with the money. The other 49 are opened one by one, none of them have the money, until only one of the others are left. So at this point you have the one suitcase you initially picked and still have, and there is one other remaining unopened suitcase. One must have the money. What is the probability yours has the money?

Question 2. Same as the above with a twist. After you pick your suitcase, 25 of the other suitcases are put into an adjacent room. So now there are 25 suitcases in each room - both rooms have a 50% probability of having the suitcase with the money. One suitcase in each room is simultaneously opened. No money is found, so one more in each room is opened etc. until there are only two suitcases left - the one you initially picked and still have in one room, and one other remaining unopened suitcase in the other room. What is the probability of the money being in your room? What is the probability of the money being in your suitcase?

If the probability of the money being in the suitcase you picked (after 48 of the original 50 were found to have been empty) is different in Case 1 than it is in Case 2, explain why.
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April 16th, 2013, 07:33 PM   #2
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Re: Probability Question

I realized I failed to include an important factor. Assume there is no pre-knowledge of where the money is as the suitcases are opened. Assume it is a random outcome that results in it being down to two suitcases. Thanks.
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April 17th, 2013, 03:50 AM   #3
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1.  The last of the others has probability 2% of having the money, so the chance that your suitcase has the money has risen to 98%.
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April 17th, 2013, 12:16 PM   #4
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Re: Probability Question

Since the 48 suitcases were opened at random, so that most (96%) of the time the money would turn up in one of them, the two remaining suitcases are equally likely to have the money. The two situations described make no difference.

You have to be careful not to mix this up with the Monte Hall problem, since in that case the opening is deliberately avoiding the money.
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April 17th, 2013, 09:40 PM   #5
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Correct!
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