Anindya Madhudor wrote:The governor has decided to pardon one of the three prisoners (A, B, C) who are on death row and informs the prison warden about his decision. Prisoner A asks the warden which prisoner will be pardoned and the warden informs him that B is to be executed. What is the updated probability of A being pardoned?
A. 1/2
B. 1/3
C. 1/6
D. 2/3
E. 1/4
OA: B
This is a variation of the Monty Hall problem, a somewhat famous question that appeared in 1975. The original question is:
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. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Answer: [spoiler]Yes, you should switch your choice. If you switch your choice to door #2, the probability is 2/3 that you'll win the car. If you stay with door #1, the probability is 1/3 that you'll win the car. [/spoiler]
More here:
https://en.wikipedia.org/wiki/Monty_Hall_problem
If you read the Wikipedia article, you'll see that the question stumped a LOT of people, including several mathematicians. As such, I don't think this question is within the scope of the GMAT.
Yes, I know a lot of people will argue that it only makes sense that, if the probability of prisoner A getting pardoned is 1/3 BEFORE asking the warden, then the probability should remain 1/3 AFTER the warden reveals that prisoner B is NOT pardoned. However, I'm not certain that this conclusion is as obvious as some people might believe.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
