1.You are in a game show! There are 10 closed doors, 0 leads to nothing and 1 leads to an expensive sports car.

Question

Q.

You are in a game show! There are 10 closed doors, 0 leads to nothing and 1 leads to an expensive sports car. You are allowed to pick a door and earn the sports car if it’s behind the door you choose. You choose a door and the host tells you he was preauthorized to make your chance of winning better! You have two options.
Option 1: Get the right to open two doors and win if the car is behind either of the ones you open.
Option 2: Have the host open 5 empty doors [None of them the one you had choose] and then get the right to switch if you want.
If you want to win the car, what should you do?

1.   Go with option 2 and switch
2.   You should be indifferent
3.   Go with option 2, then don’t switch
4.   Go with option 1

Comments

if i choose option A,then my probability is 2/10 i.e 1/5 cuz i am getting 2 chances

if i choose option B and dun switch---

i have chosen 1 door already,and host opens 5 empty doors,and if i dun switch then my chnace of winnig should be 1/5 because now sample space has been reduced to 5 doors only.

and if i choose option B and switch then then again,my chance of winning is 1/4 as there are total 4 doors to choose from because one door i had already chosen ,now i have to choose among 4 t0 switch and prize is behind 1 door only..

so,answer should be-i should go with option 2 and switch

whats wrong in my approach..pls correct me