Certainly, let's break down the expression for calculating binomial probabilities:
The binomial probability expression is given by:
[tex]\[ {}_n C_k \cdot p^k \cdot (1-p)^{n-k} \][/tex]
Here’s what each variable represents:
1. [tex]\( n \)[/tex] represents the number of trials/experiments. In a binomial setting, this is the total number of times you repeat the experiment or trial.
2. [tex]\( p \)[/tex] represents the probability of success on a single trial. This is the likelihood that a single trial will result in success.
3. [tex]\( k \)[/tex] represents the number of successes in [tex]\( n \)[/tex] trials. This is the number of times the desired outcome (success) occurs out of the total trials.
So, putting this together, the expression is used to determine the probability of having [tex]\( k \)[/tex] successes in [tex]\( n \)[/tex] independent trials, where each trial has a success probability of [tex]\( p \)[/tex].
