Binomial Distribution Formula

If

1. Fixed number of trials
2. Each trial is independent
3. There is a binary outcome

$$P(B(n,p)=k)=C(n,k)\cdot p^k\cdot (1-p{)}^{n-k}$$

where

• $P(B(n,p)=k)$ is the probability that given $n$ trials, $k$ successes will be achieved
• k = # of “successes”
• $p$ = probability of a “success” on a single attempt
• $n$ = # of trials