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Math Help - probability , game show

  1. #1
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    probability , game show

    A contestant on a quiz show is asked to choose one of three doors. Behind one of the doors is the star prize of a sports car, but behind each of the other two doors there is a toy car.
    The contestant chooses one of the three doors.
    The host then opens one of the remaining two doors and reveals a toy car. The host then asks the contestant if they want to stick with their first choice or switch to the other unopened door.
    State what you would recommend the contestant to do in order to have the greatest probability of winning the sports car. Show your working clearly.
    I dont really know how to start, cause I have no idea what the tree diagram should look like. Can anyone show me ?

    I know that the probability of him winning the car is 1/3 prbability of him winning the toy cars is 2/3

    thanks
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  2. #2
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    This is worn out problem. See Monty Hall
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  3. #3
    Moo
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    P(I'm here)=1/3, P(I'm there)=t+1/3
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    You can find a tree diagram in the wikipedia page.

    Also, you must precise whether the host knows where the car is or not. It then changes the probability.
    Again, this is explained in the wikipedia page
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