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my brother in law posed the following to me :

A contestant on a game show is presented 3 doors, one of which

has a car behind it and two do not. The contestant is asked to pick one. After choosing a door, the host then opens one of the two doors not picked by the contestant. The door opened does NOT have a car behind it.

The contestant is now given the option of keeping his original door choice, or trading for the other remaining unopened door.

Now, here is the question :

Is there a higher probability that the car will be behind the remaining unopened door, behind his original door choice, or neither ?

( we have differing opinions ) Can anyone answer this ? Please provide a clear scientific explanation, as we got into a rather heated debate over this. If either door does have a better probability, can it be quantified ?

thanks in advance

Tom

A contestant on a game show is presented 3 doors, one of which

has a car behind it and two do not. The contestant is asked to pick one. After choosing a door, the host then opens one of the two doors not picked by the contestant. The door opened does NOT have a car behind it.

The contestant is now given the option of keeping his original door choice, or trading for the other remaining unopened door.

Now, here is the question :

Is there a higher probability that the car will be behind the remaining unopened door, behind his original door choice, or neither ?

( we have differing opinions ) Can anyone answer this ? Please provide a clear scientific explanation, as we got into a rather heated debate over this. If either door does have a better probability, can it be quantified ?

thanks in advance

Tom

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