If the odds in favour of Neil beating Joe in a checker game are 5 to 4. What is the probability that Joe will win an upset victory in a best-of-five checker tournment?
Joe's prob of winning is 4/9
Neil's is 5/9
So how can Joe score an upset ?(must win 3 games)
No losses: JJJ = (4/9)^3
one loss: NJJJ JNJJ JJNJ = 3(5/9)(4/9)^3
two losses: NNJJJ NJNJJ NJJNJ JNNJJ JJNNJ JNJNJ = 6(5/9)^2(4/9)^3
I get a total of .39669 but I suggest you check my arithmetic.