Monty hall!

Logic Level 1

On a game show there are three doors. Behind one door is a new car and behind the other two are goats. Every time the game is played the contestant first picks a door. Then the host will open one of the other two doors and always reveals a goat. Then the host gives the player the option to switch to the other unopened door. Should the player switch?

No Yes

2 solutions

Mohammad Khaza
Feb 7, 2018

$\text{if he doesn't switch,}$

$\text{the probability of winning a car is }$ $\frac{1}{3}$

$\text{now,if he switches.}$

$\text{the chance of winning a car is }$ $\frac{2}{3}$

as, $\frac{2}{3}>\frac{1}{3}$ , $\text{he must switch}$

Kenny O.
Sep 1, 2017

The chance of the chosen door has the car: $\frac{1}{3}$
The chance of the other 2 door having the car: 1- $\frac{1}{3}$ = $\frac{2}{3}$
When one of the 2 doors is revealed to have the goat, the chance of the second door has $\frac{2}{3}$ as:
The chance of the 2 doors having the car is equal to $\frac{2}{3}$ and the revealed door already has a 0 chance.
If he switches, the chance of winning is $\frac{2}{3}$ , whereas the chance of winning if he doesn't switch is $\frac{1}{3}$

Does it help in reality as well ?

Kaushik Chandra - 3 years, 9 months ago

Theoretically, yes.

Kenny O. - 3 years, 9 months ago

Monty hall!

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