My office is on the 5th floor of Swapnalok Complex in Secunderabad. Everyday in the lift I have fellow passengers who get 'uplifted' with me. Every once in a while it makes me wonder on a problem of probability. Here are a few samples:
1. There are 8 floors in the Complex and my office is on the 5th floor. If 5 of us board the lift, then what is the probablity that no one will get down before me? (assuming people only get down and not get in after we start from Level 0)
2. If there are 3 'lights on' in the lift (after we start). Then what is the probability that 1 person wil get down with me?
It keeps me occupied for the time I spend in the lift. Do you have the answers?
3 comments:
I think you need to give the number of people who work on each floor to give a correct answer to your questions :)
Anyway, good show on reviving the blog!
I dont think we need that data. I have looked at the problem differently.
If 4 people are to get down between floors 1 and 4, how many ways can that happen... etc etc...
1. None of the 4 people must get down before you. Hence all 4 must get down at 5th/6th/7th/8th floor.
Probability that a person gets down at 5,6,7,8th floor is 1/2
Hence P that he does not get down in 1,2,3,4 is 1/2 (obviously)
Since there are 4 of 'em, the probability that all 4 do not get down in 1,2,3,4 floor is 1/2^4 which is 1/16
Answer: 1/16
2. 1 of the lights will be on because of you pressing 5. So, technically among the remaining 4 guys:
a. 1 of em must again press 5 (or not press, it does not matter anyway)
b. The other 3 must press the remaining 2 lights. This can happen with 2 getting down in floor X and 1 getting down in floor Y wherein X and Y are not 5.
**The probability that 2 guys select the same floor X is 1/8*1/8 and floor X can be selected in 7 ways. Therefore, actual probability is 7/64
** The probability that the other guy selects floor Y is 1/8 and Y can be selected in 6 ways (excluding 5th floor and Xth floor)
Therefore probability that he selects Y is 6/8 or 3/4
** Probability that 4th person will select 5th floor is 1/8
*** Hence combined probability that 2 persons will select floor X, 1 will select floor Y and 1 will select 5th floor is
7/64*3/4*1/8 = 21/2048
Are these answers correct?
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