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I came across this interesting problem the other day. Later a watched a movie and this problem was actually in the movie. Take a look! In the game show "Let's Make a Deal", a contestant is presented with 3 doors. There is a prize behind one of the doors, and the host of the show knows which one. When the contestant makes a choice of door, at least one of the other doors will not have a prize, and the host will open a door (one not chosen by the contestant) with no prize. The contestant is given the option to change his choice after the host shows the door without a prize. If the contestant switches doors, what is the probability that he gets the door with the prize? We define the events A = prize door is chosen after contestant switches doors, B = prize door is initial one chosen by contestant. Then P[B] = 1/3, since each door is equally likely to hold the prize initially. To find P[A] we use the Law of Total Probability. P[A] = P[A|B]*P[B] + P[A|B']*P[B']. This... read more

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