Hi guys. I've been pretty inactive in the past few weeks due to finals and other things coming up. Anyways, here's my question:
The problem I'm about to describe might seem a little obscure. I'll give an example after so that it's more clear.
If there are two events that can occur, event A and event B, and the likelyhood of event A happening is n (where n is some rational number such that 1 < n < 0) and the odds of B happening is 1 - n. What are the odds of event B happening "r" times out of "m" trials, where the order of wins and losses does not matter?
Example: In a rigged game of "Heads or Tails," the odds of "winning" (you choose heads and it comes heads or you choose tails and it comes tails) is 75% or 3/4 (so that 3 out of 4 times that you play you will win no matter which side of the coin you chose). What are the odds of loosing 10 times (total, not necessarily in a row) if you play the game 12 times?
Hope that made sense, and thanks for the help.