Find the probability of opening of the door?

238 views

There are 4 people in a closed room and you are waiting outside to enter into the room. You can enter only when one of them opens the door. The probability that somebody will open the door is 1/2. Now what is the probability that the door will be opened so that you can go inside?

posted Jan 25, 2014

+1 vote

Probability of room 1 is open and rest all is closed - 1/2*1/2*1/2*1/2 = 1/16
Similarly
Probability of room 2 is open and rest all is closed - 1/2*1/2*1/2*1/2 = 1/16
Probability of room 3 is open and rest all is closed - 1/2*1/2*1/2*1/2 = 1/16
Probability of room 4 is open and rest all is closed - 1/2*1/2*1/2*1/2 = 1/16

Total probability = 4/16 or 1/4

Similar Puzzles

I have two coins.
* One of the coin is a faulty coin having tail on both side of it.
* The other coin is a perfect coin (heads on side and tail on other).

I blind fold myself and pick a coin and put the coin on table. The face of coin towards the sky is tail.

What is the probability that other side is also tail ?

A and B have two children. The probability that the first child is a girl is 50%. The probability that the second child is a girl is also 50%. A and B tell you that they have a daughter.

What is the probability that their other child is also a girl?

You are on a game show and there are three doors. The presenter tells you that behind one of doors there is a car and behind the other two are goats. If you pick the car you win it. After you have picked a door the presenter opens a different door with a goat behind it, he then gives you the chance to change what door you open. What should you do?

Hint: It is not 1/2 as you would first think.