You already learned the expression for calculating binomial probabilities:

[tex]\[ { }_n C_k(p)^k(1-p)^{n-k} \][/tex]

What does each variable represent?

- [tex]\( n \)[/tex] represents the [tex]\(\square\)[/tex]
- [tex]\( p \)[/tex] represents the [tex]\(\square\)[/tex]
- [tex]\( k \)[/tex] represents the [tex]\(\square\)[/tex]

Question

07-08-2024
Mathematics

Answered

You already learned the expression for calculating binomial probabilities:

[tex]\[ { }_n C_k(p)^k(1-p)^{n-k} \][/tex]

What does each variable represent?

- [tex]\( n \)[/tex] represents the [tex]\(\square\)[/tex]
- [tex]\( p \)[/tex] represents the [tex]\(\square\)[/tex]
- [tex]\( k \)[/tex] represents the [tex]\(\square\)[/tex]

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-08-07T06:02:24-04:00

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].