# Monty Hall

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat.

What is the probability that the chosen door is open and you will see them in the car?

What is the probability that you change decision and open the remaining doors and see car?

Result

p1 =  33.3 %
p2 =  66.7 %
result if staying at door :  0 1

#### Solution:

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 car goat
goat car goat goat car
goat goat car goat car

$p_2=2/3 \cdot \ 100 = 66.7 \%$

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