3 goats behind 3 gates. One of them is black. You pick one you think is black. Then the host opens the gate and the goat behind it is not black. Do you switch your choice or not?
The key point is whether the host has knowledge of the color of goats or not. If he does, your orignal choice still has 1/3 chance of being right. if he doesn't, your original choice has 1/2 chance.
In KMM's question, there is no host with knowledge of the other child picking the family for you. The probability of the other child being a boy is 1/2. If there is a host with knowledge of both children, picking a family having at least one boy, and arrange you to meet him, the answer changed to 1/3.
The key point is whether the host has knowledge of the color of goats or not. If he does, your orignal choice still has 1/3 chance of being right. if he doesn't, your original choice has 1/2 chance.
In KMM's question, there is no host with knowledge of the other child picking the family for you. The probability of the other child being a boy is 1/2. If there is a host with knowledge of both children, picking a family having at least one boy, and arrange you to meet him, the answer changed to 1/3.
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