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There are 20 floors in a building. If you're on an elevator and you're trying to get to the 20th floor, what is the probability that 4 people ahead of you click the 20th floor before you do? Assuming you click last.10 Answers
assume there is one button for each floor, so 20 buttons. a person can press any 1 button out of the 20, prob is 1/20. Since there are 4 people, so1/16000
These are independent events so the chances of one person before you going to the 20th floor is 1/20. Since this happens 4 times before you the probability is 4*(1/20) or 1/5.
The above two are close, but wrong.. There are 20 buttons, thus 20 choices, sure. But you are getting on at one of the floor. No body will press the button for the floor they get on.. Thus, there is really only 19 choices. P = (1/19)^3 (Independent events mean (1/19)(1/19)(1/19)).
1/19 + 1/18 + 1/17 + 1/16 assuming that there were no repeated destinations.
based on question: P(all 4 ahead of you want to get off on 20th fl) = (1/19)^4 real life(all 4 want to get off on 20th fl, and one of them is the first person press the button to 20th fl, and that leave all others, including you, stay still): (1/19) * (1/4)
about 20% is the right answer. I am surprised with some of the answers, they are all very small possibilities (some less than 1%).
I'm quite sure you are all wrong: The real probability is 1 - P(nobody pushes 20) = 1 - (18/19)^3 = 15%
If one of the 4 press the button for the 20th floor then the others won't have to do anything. The chances of one of them pressing 20th is: 1/19 + 1/19 + 1/19 + 1/19 = 4/19
The answer is 1-(19/20)^4