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I asked the following question on an exam and want to verify I have the correct answer before marking it. “Your friend has three laptops that he wants to get rid of. He offers one of them to you. He then remembers that two of them have batteries that only hold a few minutes of charge – but one of them is fine. He’s not sure which one is still good because all the batteries are currently empty. But he says you must select one now. So, you decide to take the silver one. But then he suddenly remembers that his brother told him that the black one is bad and informs you of the fact. He then says, do you still want the silver one, or do you want to swap it for the space grey laptop? What should you do?”

Is this the Monty Hall problem (meaning you should switch) or is it different since the friend only remembers one of the bad laptops after the choice was made? I’m marking this question as a Monty Hall type problem - but I thought I’d bounce it off some math wizzes just in case. I’m thinking maybe it’s 50-50 because the friend would have told the player that he had chosen a bad laptop if the player had chosen the black one.

Aleks
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2 Answers2

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The way the question was stated does not appear to be the Monty Hall problem. Indeed, as you mention, it reads as if the brother remembered that the black laptop was bad (randomly). Then there is a 50/50 chance for the two remaining laptops to be bad.

An important aspect of the Monty Hall problem is that the 'door opened' is not random - it is based on the choice (i.e., if the contestant chooses a door with a 'goat', the host will reveal which of the other two doors holds the other 'goat').

holger3000
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It is not the same as Monte Hall for the reason you have stated. If your friend had chosen the black one at first, you would have told him to pick one of the others. For Monte Hall, if the contestant picks the good door, Monte Hall would not infor him.

herb steinberg
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