I have the following question in an exam paper and I don't know exactly how to treat it. I would appreciate a hint with regards to what formula to use or such:
A bag contains 5 red balls and 1 black ball. Balls are randomly drawn from the bag until the black ball is found, and the number of draws require is noted. How much greater is the expected number of draws required if any red balls from the bag is replaced rather than put to one side?
Now, I know that if there was no replacement, the black ball has a chance of 1/6+1/5+1/4+1/3+1/2 to be extracted. Please correct me if I'm wrong.
What happens when there's replacement involved?