Time remaining:
Bayesian Statistics Riddle

Statistics
Tutor: None Selected Time limit: 0 Hours

There is a car behind one of three doors.  You make a guess that the first door has the car.  After stating your guess, one of the two remaining doors open to reveal nothing.  Does your chance of getting a car increase if you decide to switch doors?

Feb 13th, 2015

suppose we have n doors, with a car behind 1 of them. The probability of choosing the door with the car behind it on your first pick, is 1n.

Monty then opens k doors, where 0≤k≤n−2 (he has to leave your original door and at least one other door closed).

The probability of picking the car if you choose a different door, is the chance of not having picked the car, which is n−1n, times the probability of picking it now, which is 1n−k−1. This gives us a total probability of

n−1n1n−k−1=1nn−1n−k−11n

If Monty opens no doors, k=0 and that reduces to 1n.

For all k>0, n−1n−k−1>1 and so the probabilty of picking the car on your second guess is greater than 1n.

If k is at its maximum value of n−2, the probability of picking a car after switching becomes

1nn−1n−(n−2)−1=1nn−11=n−1n


Feb 13th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Feb 13th, 2015
...
Feb 13th, 2015
Dec 11th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer