Question

GEOMETRIC DISTRIBUTION QUESTION:

There are 15 professors in the math department. every time tina takes a math class each professor is equally likely to be the instructor. What is the expected number of math classes which tina needs to take in order to be taught by every math professor?

Answer 1

here for first different professor expected number of math class required =1 (since any professor who comes will be different in first class)

for 2nd different expected number of classes required =1/p=1/(14/15)=15/14 (since for 2nd one probability of different professor is 14/15)

for 3rd different professor , required number =1/p=1/(13/15)=15/13

from above  e expected number of math classes to be taken

=1+15/14+15/13+15/12+15/11+15/10+15/9+15/8+15/7+15/6+15/5+15/4+15/3+15/2+15/1

=49.77 classes ~ 50 classes