You are faced with 5 doors. Behind one door is a car, and behind the other four are goats. You pick one door. The host, who knows where the car is, then opens 3 of the remaining doors, all revealing goats. You are then offered the chance to switch your choice to the one remaining unopened door. What is the probability of winning the car if you decide to switch?
Show answer & explanation
Correct answer: C
Explanation
Probability that the car is behind the initially chosen door = 1/5
Total probability for the remaining 4 doors = 1 - 1/5 = 4/5
The host eliminates 3 of these 4 doors (those concealing goats), leaving only one unopened door.
The entire 4/5 probability associated with that group now shifts to this single remaining door.
Probability of winning by switching to this door = 4/5