Originally Posted by

**ANDS!** 1. A little weird, will have to think about it for a minute.

2. The question doesn't say Miranda or Rob has to throw the winning toss, so on either persons turn there are only four possible outcomes: {HH, TT, TH, HT}. Thus on any one turn, there is a 0.5 chance the game will end in a win for any one of the players, which makes sense as there is a 0.5 chance the game will end on the "first" toss:

$\displaystyle 1-\frac{1}{2^{1}} = 0.5$

This is a sort of "cummulative" (well it is) distribution for "the probability that that game will end in 'n' number of turns"; which is what the question is asking. For example, what is the probability that the game will end at or before the 2nd turn - 0.75.