I want to share a question that is really old (older than me, actually). It is from the June 1972 paper. As most students know, Maclaurin’s series was tested in last year A’levels Paper 1 as a sum to infinity. And this DRV did the same thing. Here is the question.

A bag contains 6 black balls and 2 white balls. Balls are drawn at random one at a time from the bag without replacement, and a white ball is drawn for the first time at *R* th draw.

(i) Tabulate the probability distribution for *R*.

(ii) Show that E( *R* ) = 3, and find Var( *R* ).

If each ball is replaced before another is drawn, show that in this case E( *R* ) = 4.