Sure, let's break down the expression for calculating binomial probabilities step-by-step:
The expression is:
[tex]\[ { }_n C_k \cdot (p)^k \cdot (1-p)^{n-k} \][/tex]
Here, each variable represents the following:
1. [tex]\( n \)[/tex] represents the number of trials. This is the total number of times an experiment or a process is conducted.
2. [tex]\( p \)[/tex] represents the probability of success on a single trial. This is the likelihood of achieving a successful outcome in each individual trial.
3. [tex]\( k \)[/tex] represents the number of successes. This is the count of successful outcomes that you are interested in observing within the [tex]\( n \)[/tex] trials.
So, to summarize:
- [tex]\( n \)[/tex] represents the number of trials.
- [tex]\( p \)[/tex] represents the probability of success on a single trial.
- [tex]\( k \)[/tex] represents the number of successes.
