This is a really dumb question. I haven't been in school for a good number of years and I can't remember the formula for a simple probability problem. For example if I have four coins, what are the odds that at least 2 of them are tails after 1 flip of each coin. Now I know the answer is 11/16 but I can't figure out the middle part. By simple counting I know that:
Chances of getting exactly 0 tails out of 4 is 1/16
Chances of getting exactly 1 tail out of 4 is 4/16
Chances of getting exactly 2 tails out of 4 is 6/16
Chances of getting exactly 3 tails out of 4 is 4/16
Chances of getting exactly 3 tails out of 4 is 1/16
The thing I can't remember is how to get the 4/16, 6/16 mathematically. Yeah it's real easy to count for small number sets, but what if I'm flipping 400 coins?
Chances of getting exactly 0 tails out of 4 is 1/16
Chances of getting exactly 1 tail out of 4 is 4/16
Chances of getting exactly 2 tails out of 4 is 6/16
Chances of getting exactly 3 tails out of 4 is 4/16
Chances of getting exactly 3 tails out of 4 is 1/16
The thing I can't remember is how to get the 4/16, 6/16 mathematically. Yeah it's real easy to count for small number sets, but what if I'm flipping 400 coins?