Question

Combination of random variables

Suppose that the Ben & Jerry’s ice cream has ten flavors. Every week you ask your roommate Joe to randomly pick one flavor for you when he does grocery shopping. Each flavor (including those you have already tried) is picked up equally likely. How many weeks on average do you need to try all the flavors?

Answer 1

here as there are 10 different flavours available ; 1st different flavour is picked on 1st week ; 2nd different will take approx further 10/(10-1) weeks and so on

here number of weeks to collect all n flaovours=10*(1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10)

=29.29 weeks

(this is a version of standard coupon collector problem)