a little probability question

WeeG

TS Contributor
#1
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 ?

cheers
 

fed1

TS Contributor
#2
Does anyone else think the 8 and 10 are in the wrong places in answer e.

Pr( no one choose floor j ) = Pr(Aj) = Bin(n = 10, x = 0, p = 1/8) = (7/8)^10.

E( Sum( Aj ) from 1 to 8 ) = 8 (7/8)^10