Challenge Problem #3
We saw in lecture 24 that there is an experiment with 256 outcomes. One outcome T has probability about 5%, and the remaining 255 outcomes have probability 95/255% or about .04%. We don't know the value of the higher-probability outcome. We are wondering how many trials are required to find it.
Your job is to find a formula to determine this. Give a formula (or a program, if you prefer) which computes the probability that T will be the majority result in our trials, given n trials. (So, your parameter is n, and the output of your formula is p.)
Example (which is not correct, by the way): if I run 20 trials, then with probability .62, T will be the majority element in the outcomes of those trials.
You could also graph this function if you wanted to really be snazzy.
Extra Credit Points: 10