The probability that any PARTICULAR floors are not used, is
As there are ways to choose floors, it is clear that the probability of floors not being chosen is just
Hence just sum the above for X in 1-8 and you should get the correct answer.
An elevator goes from the ground floor up to the 8th floor (8 floors in total). In the elevator 10 people. Each one of them choose randomly and independently with the other people in which floor to get off the elevator. The expected value (mean) of the number floors in which no one came off at is:
a. 6 b. 8 c. 8*(7/8)^10 d. 10*(1/8)^10 e. 10*(7/8)^8
the correct answer should be "e". why ?
I know, I just thought that if I see an example of how you calculate P(X=0) I can calculate for the rest of X=1-8 and then calculate E(X). I said that 'e' is the correct answer, but I am starting to wonder, according to what you guys said, that it's not true, that 'c' is the correct answer ! am I right ?
Yes "c" is the answer.
Can you figure out why the probability that any given door not being chosen is ?
Hint: First ask yourself what is the probability of a given person NOT choosing this floor? Then use this to determine the probability that all 10 of them don't choose it.
I already described in my first post how to calculate each P(x=i) for i in 1-8, but this is long and unnecessary.