Solution:Amazon puzzle: find probability of men to go in room

Solution:

1 - 1/2 * 1/2 * 1/2 * 1/2 =>  15/16

explanation:

It is the combined probability of all possible events minus the probability that all four people will NOT open the door (1/2)^4. Another way to look at this problem would be to take the sum of the probabilities of all possible ways that the door will be opened:

P[person a opens the door] = 0.5

+ P[2 people open door] = P[person a] * P[person b] = 0.25

+ P[3 people open door] = P[person a] * P[person b] * P[person c] = 0.125

+ P[all 4 open door] = P[person a] * P[person b] * P[person c] * P[person d] = 0.0625

= 0.5 + 0.25 + 0.125 + 0.0625 = 0.9375 that the door will be opened, or 15/16.

POST YOUR OPINION IF YOU HAVE BETTER SOLUTION