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## Homework Statement

Derive the bernoulli binomial distribution by generalizing the probability of a coin flip.

## P(k, n) = \binom{n}{k}p^{k}q^{(n-k)} ##, q = p - 1

## Homework Equations

**Combination: ## \binom{n}{k} = \frac {n!} {k!(n-k)!} ##**

**Prob. of coin flip: ## \frac {\binom{n}{k}} {2^n} ##**

3. The Attempt at a Solution

3. The Attempt at a Solution

I don't have much background in statistics

**,**so I'm trying to figure out how these distributions were derived and such.

Looking at it in terms of a game, like flipping a coin, where heads is a win, tails is a lose, I don't understand things like why the probability of getting a win is ## p^{k} ## , or why the probability of losing is ## (p-1)^{n-k} ##. Then after that, why is the ## \binom{n}{k} ## even included in the equation.

I've been reading books, and articles, and I'm just not really wrapping my head around how multiplying the combination of ## \binom{n}{k} ## by the probability of winning by the probability of losing, even gives us the probability of the outcome.