I am learning about the binomial distribution, and I think I've understood the concept. However, there is one thing that is making me very confused:
There are $41$ trials and each trial will yield one of two results: Result $X$ or $Y$. The observation is that $14$ out of $41$ trials brought $X$. So the probability of occurring $X$ is $\dfrac{14}{41} \approx 0.341$.
Now, when I used binomial distribution formula where $k = 14$, $n = 41$ and probability $= 0.341$ (following is a function of R language to get binomial distribution):
dbinom(14, 41, 14/41)
it brings the result/probability $0.1304709$.
I am unable to understand if as per our observation probability is $0.341$ then applying binomial formula, the result should also be the same probability.
Thanks in advance for your explanation.
PS: Please note that I am basically a software engineer and not very good at maths, so the simpler the answer the easier will it be for me to understand.