You are on a game show and you are given the choice of three doors. behind one door is a car (the main prize). behind each of the other two doors is a goat (you lose). you pick a door and the host (who knows what's behind the doors) opens another door which has a goat behind it. the host asks you if you want to stay with your original choice or to switch to the other unopened door. is it better to stay or switch doors? which choice has a higher probability of winning or does it not matter?

You need to switch doors.

Switching the door has higher probability of winning.

Step-by-step explanation:

Consider the provided information.

Suppose there are 3 doors, A, B and C

Behind one door is a car that means the probability of getting a car is 1/3

Suppose you select door A

The probability that the it has a goat is 2/3. That means it is very likely to be a goat behind door A.

The other two door(B and C) are more likely to contain a goat and car.

The host opens another door which has a goat behind it. Let say he open the door B.

Now there is more chance to be a car behind it as compare to the previous choice.

Thus, you need to switch doors.

Switching the doors will gives you 2 in 3 chance of winning while staying with same door will gives you 1 in 3 chance of winning.

Switching the door has higher probability of winning.