2007 iTest Problems/Problem 59

Problem

Let $T=\text{TNFTPP}$ . Fermi and Feynman play the game $\textit{Probabicloneme}$ in which Fermi wins with probability $a/b$ , where $a$ and $b$ are relatively prime positive integers such that $a/b<1/2$ . The rest of the time Feynman wins (there are no ties or incomplete games). It takes a negligible amount of time for the two geniuses to play $\textit{Probabicloneme}$ so they play many many times. Assuming they can play infinitely many games (eh, they're in Physicist Heaven, we can bend the rules), the probability that they are ever tied in total wins after they start (they have the same positive win totals) is $(T-332)/(2T-601)$ . Find the value of $a$ .

Solution

17

2007 iTest (Problems, Answer Key)
Preceded by: Problem 58	Followed by: Problem 60
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4

Page

Toolbox

Search

2007 iTest Problems/Problem 59

Problem

Solution

See Also