# Find the probability of opening of the door?

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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

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