Sue and Bob take turns rolling a 6-sided die. Once either person rolls a 6, the game is over. Sue rolls first. If she doesn’t roll a 6, Bob rolls the die; if he doesn’t roll a 6, Sue rolls again. They continue taking turns until one of them rolls a 6.
Bob rolls a 6 before Sue.
What is the probability Bob rolled the 6 on his second turn?
The answer is not 5/36.
I love puzzles which are simple to state but have a fiendishly tricky or counterintuitive answer. I just threw up a page on the xkcd IRC wiki to hold some of the better ones I’ve found over the years. I’ll be adding more over the next few weeks as I remember or find good ones. Feel free to add some of your own!
Edit: Buttons and then Daniel Barkalow got the correct answer first. Here it is, rot13‘d. Check your answer against this before posting smugly or people (I) will tease you: gjb friragl svir bire gjryir avargl fvk, be nobhg gjragl-bar cbvag bar creprag.