Dartboard
Suppose you are throwing darts at a dart board and on each throw you have probability 1/20 of hitting the bulls-eye. How many darts to you have to throw on average to get the first bulls-eye?
And now as a challenging extension of this recursive approach, here’s a fascinating pair of examples.
I roll a fair 6-sided die until I get a six followed by a five. How many rolls on average does that take?
I roll a fair -sides die until I get two sixes in a row. How many rolls on average does that take?