Number of Trials Required For Brute Force Attack To Have x% Of Success?
Since nobody replied, I posted this on the Math Stack Exchange and quickly got an answer. 

For anyone that's interested, using a formula from R we get the following values:

pbinom(0,3.365231884e48,2^(-160), FALSE)   = 0.9000000000339017
pbinom(0,1.0130357393e48,2^(-160), FALSE)  = 0.5000000000001161
pbinom(0,1.46885823057e46,2^(-160), FALSE) = 0.01000000000005571