In a popular TV show, the winner of game among attendees can participate a conte

Question

In a popular TV show, the winner of game among attendees can

participate a contest for cash award. The rules are as follows: The winner can

select one of the three doors, while there is a big cash prize behind one door, and

“thank you” behind other two doors.

(a) Once the winner selects one door, the TV show host opens one of the other

two doors and shows “thank you” sign. The host will ask the winner whether

to change his/her selection. Obviously, the host knows which door behind has

the prize. Please determine the best policy for the winner, to change selection

or not.

(b) Once the winner selects one door, an earthquake happens and thus one of the

other two doors randomly opens to reveal a “thank you” sign. The host will

ask the winner whether to change his/her selection. Please determine for the

winner, to change selection or not.

Explanation / Answer

a)The best policy for the winner is to change the selection

Let us consider there are 3 doors namely A, B and C.out of the three doors behind one door there is a cash Prize and behind the other two doors are "thank you" sign.

1)No doors are opened for the Winner The TV show host offers no help in picking a door. In this case, it is obvious that the odds of picking the correct door are 1/3.Let the winner selects door A

2)The Tv show host then opens one of the remaining two doors i.e. door C, revealing a "thank you" sign to be behind there, and asks winner if he/she would like to change his selection.

The winner does change his/her selection to door B, because, the odds are now in favor of door B, with a 1/3 chance of winning if door A is picked and 2/3 chance of winning if door B is picked.

b)The winner should obviously change his selection to increase his/her chances of winning.

)No doors are opened for the Winner The TV show host offers no help in picking a door. In this case, it is obvious that the odds of picking the correct door are 1/3.Let the winner selects door A

2)Due to the earthquake, one of the remaining two doors randomly opens i.e. door C, revealing a "thank you" sign to be behind there, and the host will ask the winner if he/she would like to change his selection.

The winner does change his/her selection to door B, because, the odds are now in favor of door B, with a 1/3 chance of winning if door A is picked and 2/3 chance of winning if door B is picked.

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