Certainly! Let’s break down what each variable in the binomial probability expression represents:
1. [tex]\( n \)[/tex] represents the number of trials. This is the total number of times you perform an experiment or the number of observations in your binomial experiment.
2. [tex]\( p \)[/tex] represents the probability of success on any given trial. This is the likelihood that any single trial will result in a success.
3. [tex]\( k \)[/tex] represents the number of successes. This is the number of times that you achieve a success in [tex]\( n \)[/tex] trials.
So, the expression for calculating binomial probabilities:
[tex]\[ { }_n C_k \cdot p^k \cdot (1-p)^{n-k} \][/tex]
uses these variables where:
- [tex]\( n \)[/tex] is the number of trials,
- [tex]\( p \)[/tex] is the probability of success on any given trial,
- [tex]\( k \)[/tex] is the number of successes.
