In the Monty Hall game, a new car is hidden behind one of three closed doors whi
ID: 2079293 • Letter: I
Question
In the Monty Hall game, a new car is hidden behind one of three closed doors while a goat is hidden behind each of the other two doors. Your goal is to select the door that hides the car. You make a preliminary selection and then a final selection. The game proceeds as follows: You select a door. The host, Monty Hall (who knows where the car is hidden), opens one of the two doors you didn't select to reveal a goat. Monty then asks you if you would like to switch your selection to the other unopened door After you make your choice (either staying with your original door, or switching doors), Monty reveals the prize behind your chosen door. To maximize your probability P[C] of winning the car, is switching to the other door either (a) a good idea, (b) a bad idea or (c) makes no difference?Explanation / Answer
Its question more of intelligence than just mathematics.
Given rules of the Game:
-> Select a door out of 3 (of which behind only one door there is a prize which is a Car, and rest of the doors have goats)
->The host, Monty hall selects one of the other doors to reveal the presence of goat
->Here starts the game of intelligence and confidence , Monty hall asks you to change or withstand with your original decision. Monty will reveal the prize behind your chosen door.
Solution is : 1. To choose a door out of 3 doors, = 1/3.
2. Monty hall will chose one door out of 2 doors = 1/2
Here you need to take a chance, and prove your intelligence choosing whether to withstand with your decision or to change.
Chances of winning:
A. -> If the door chosen by you contains the Car, then you will win, your win probability is 1/3.
B.-> If the door chosen by you doesn't contain car, then Monty hall as already he knows which door contains car, so he might of chose that one only and may leave the door which contains goat.
i. Since he has chosen one door, we may feel that the other door doesnt contain the Car.
3 types of people.
1. Idiot
2. Intelligent
3. Most intelligent
Idoit will chose the other door and loose.
Intelligent person will also chose the other door(3rd one) but the car will be there in other door, and loose.
Most intelligent person will withhold to his own decision.
Winning probability= Chosing a door * Winning the car + Missed door * loosing the car
P(C) = (1/3)*(1/3) + (2/3)(2/3)
= 5/9
Its a fact of luck and intelligence.
Happy chegging!!!