I would like some help reviewing Binomial Distribution, specifically when using the Probability Mass Function equation. I read the Wikipedia page and I'm not understanding how to use the Probability Mass Function equation.
K is the number of successes, right? N is the number of trials, right? N might be the number of dice rolled, coins flipped, tests performed, etc. But when I plug in the numbers for my variables I'm not getting results I would've expected.
Like for example I recall encountering an explanation about coin flips, if you flip a coin there's a 50/50 chance of getting heads, right? So, if you flip two coins there's a 75% chance of getting heads with at least one of the coins right? Or perhaps a better way of saying that would be that there's only a 25% chance of both coins landing heads up or both tails up, right?
Though when I input K = 1 (at least 1 heads up) and N = 2 (two coins flipped) I just get .125. I know that each individual coin flip has the same percent chance of getting a given result assuming it's a perfectly balanced coin that never lands on its edge, but wouldn't more coins or more trials or whatever naturally increase the likelihood of a given event?
Sample Probability question: what is the percent chance of seeing at least one heads up result if you flip two coins at the same time?
My work: (.5^2)(1-.5)^2-1 = .25(.5)^1 = .125
My thoughts: There cannot be a 12.5% chance of seeing at least 1 heads up toss between 2 flipped coins. I know that I'm doing something wrong, but I don't know what. (I got two other responses regarding cumulative distribution functions, but I am not familiar with those).