How Does the Binomial Coefficient Calculate Combinations?

Thread starter g.lemaitre
Start date Oct 2, 2012
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Binomial Function Probability Probability function

In summary, a Binomial probability function is a mathematical model used to calculate the probability of a certain number of successes in a fixed number of independent trials. To use this function, you need to know the number of trials, the probability of success in each trial, and the number of successes you are interested in. It differs from a Binomial distribution, which is a graphical representation of the possible outcomes and their probabilities. This function has various real-life applications in fields such as business, economics, and science. It is only applicable to discrete data and is not suitable for continuous data.

Oct 2, 2012

g.lemaitre

Homework Statement

Homework Equations

The Attempt at a Solution

do you see where it says 5 over 2 = 10 and 5 over 3 = 10. How? I don't get what they're doing.

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Oct 2, 2012

g.lemaitre

never mind i got it.

n!/(x!(n-x)!)

Related to How Does the Binomial Coefficient Calculate Combinations?

1. What is a Binomial probability function?

A Binomial probability function is a mathematical model used to calculate the probability of a certain number of successes in a fixed number of independent trials. It is based on the binomial distribution, which describes the probability of two possible outcomes (success or failure) in a single trial.

2. How do you calculate the probability using the Binomial probability function?

To calculate the probability using the Binomial probability function, you need to know the number of trials, the probability of success in each trial, and the number of successes you are interested in. The formula is P(x) = nCx * p^x * (1-p)^(n-x), where n is the number of trials, p is the probability of success, x is the number of successes, and nCx is the combination formula.

3. What is the difference between a Binomial probability function and a Binomial distribution?

The Binomial probability function is a mathematical equation used to calculate the probability of a certain number of successes, while the Binomial distribution is a graphical representation of the possible outcomes and their respective probabilities. The Binomial distribution is a visual representation of the Binomial probability function.

4. What are some real-life applications of the Binomial probability function?

The Binomial probability function is commonly used in various fields, including business, economics, and science. It can be used to predict the success rate of a marketing campaign, the probability of a stock market investment yielding a profit, or the likelihood of a drug being effective in a clinical trial.

5. Can the Binomial probability function be used for continuous data?

No, the Binomial probability function is only applicable to discrete data, where there are a fixed number of trials and two possible outcomes (success or failure) in each trial. For continuous data, other probability functions such as the Normal distribution or Poisson distribution are used.