2007 iTest Problems/Problem 59
Revision as of 16:11, 14 February 2020 by Piphi (talk | contribs) (Undo revision 117753 by Bubblyducks (talk))
Problem
Let 
. Fermi and Feynman play the game 
in which Fermi wins with probability 
, where 
and 
are relatively prime positive integers such that 
. 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 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 
. Find the value of .
Solution
See Also
| 2007 iTest (Problems) | ||
| 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 | ||
