On the game show a contestant was asked to select one of three doors. Behind one

Question

On the game show a contestant was asked to select one of three doors. Behind one of the doors was a prize; while behind the other two doors were gag gifts. After the contestant made their selection, the game show host (Monty Hall) would open one of the two remaining doors to reveal one of the gag gifts. The contestant was then given an opportunity to switch doors. (For example, suppose the contestant initially selects door number 1, and then Monty Hall opens number 3 to reveal a gag gift. The contestant can then stay with door 1 or switch to door 2.)

The question is: should the contestant switch doors? Justify your answer by calculating the probability of winning the prize under both strategies.

Explanation / Answer

Out of 3 doors probability of selecting door with prize is 1/3 = 0.33

And probability of selecting gag gift is 2/6 = 0.67

After the host reveals one door with gag gift

There are 2 doors left

The probability of selecting the door with prize is 1/2 = 0.5

The probability of selecting the door with gag gift is 1/2 = 0.5

Since probability of selecting door with prize increases in second selection and probability of selecting gag door decreases the contestant may do the selection again

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