In a TV Game show, a contestant selects one of 7 doors; behind one of the doors
ID: 3363068 • Letter: I
Question
In a TV Game show, a contestant selects one of 7 doors; behind one of the doors there is an iPhone X, and behind the other 6 there are no prizes. After the contestant selects a door, the game-show host opens all but two of the remaining doors, and reveals that there is no prize behind them. Now there are 3 doors closed. The host then asks the contestant whether they want to SWITCH their choice to the any other unopened 2 doors , or STICK to their original choice. Use conditional probability to determine if the contestant should switch or stick. Also find out what will be probability of winning if the contestant always switch.
*SOLVE USING BAYE'S THEOREM AND EQUATIONS*
Explanation / Answer
IT IS A MONTY HALL PROBLEM:-
LET US CONSIDER CASE AS BELOW:-
So there are 3 cases possible for Door-1, similarly for Door-2 & Door-3.
Considering Door-1:-
On Switching as shown above 2/3 chances of winning; similarly with door 2 & door3
So Over all chances of winning is 2/3 in case of switching.
Behind door 1 Behind door 2 Behind door 3 Result if staying at door #1 Result if switching to the door offered Car Goat Goat Wins car Wins goat Goat Car Goat Wins goat Wins car Goat Goat Car Wins goat Wins car