Originally Posted by

**hong2**
Hi Roy,

this is really quite interesting. To switch or not to switch and the final answer is

YES and NO depending on the assumption:

1) YES (probability 1/3 and 2/3) if the host knows where the prize is, and your reasoning is correct.

2) NO (probability 1/2 and 1/2) when the host just makes a random pick, and my reasoning is correct.

Since your assumption is that the host KNOWS, then you are correct with your argument.

Since the host knows, this is not really a probability problem (randomness) anymore. One can argue that because of the your reasoning, the host will open an empty box to tempt the player to switch. Again it is assumed that the host was instructed to help keep the prize. Of course he could just be trying to make the show interesting. Good job though.

I have a similar problem. With a population of families with 2 children, given that one of the children is a girl, what is the probability that the other is also a girl? Seems quite simple? Have fun !

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