Wikipedial Let\'s Make a Deal is a television game show that originated in the U

Question

Wikipedial Let's Make a Deal is a television game show that originated in the United States in 1963 and has since been produced in many countries throughout the world. The program was created and produced by Stefan Hatos and Monty Hall, the latter serving as its host for many years. The program's defining game mechanism is that the other item is hidden from the trader in one of the boxes until that choice is made. The trader thus does not know if he or she is getting the real prize or a prize that is referred to as a "zonk," an item purposely chosen to be of little or no value to the trader. For simplicity, let us assume you are the trader and you are shown 3 boxes and asked to guess the one with the real prize (so the other two contain "zonk"s). 1) In the first step you choose one box, lets say box#1. The host told you that "buddy it's no good, I will make a favor for you and eliminate the last box (#3). Now you have 2 boxes: box#1 (your choice) and box #2. 2) So: would you still choose box#1? Or change your pick to bom? or it does not matter (same probability).

Explanation / Answer

We should change the box.

There are three boxes at the start and only one contains the real prize. Therefore, while choosing one box out of three, probability of getting ‘real prize’ box is 1/3=0.33

Now, suppose we choose one box, and out of remaining two, host eliminates one box which doesn’t contain real prize. So, now there are two boxes: one that we have chosen and other one. Out of these two, one box contains the real prize. So, now if we select the box, probability of getting the real prize is 0.5, which is greater than 0.33. So, success probability increases. Therefore, we should change the box.

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