Binomial Distribution Probability Calculator
What is a Binomial Distribution in Statistics
The binomial distribution is a distribution that is used when:
- there are only 2 outcomes (we call them success or failure)
- there are a number of trials (n), all are independent of one another, and
- the probability of success or failure in each trial is the same for all the trials
Examples of binomial distribution
Example 1: How many heads will you get when you toss a fair coin 10 times
The number of heads obtained when flipping a fair coin 10 times is an example of a binomial distribution. In this case, we have 10 independent trials (n = 10). The probability of obtaining a head is 0.5 since the coin only have 2 sides, and this is a fair coin, and the probability of getting a head in one toss is not affected by another trial.
Example 2: How many 6 will you obtain when you throw a fair die 50 times.
The number of 6 that you will obtain when throwing a fair die 50 times is another example of a binomial distribution. In this case, we have 50 independent trials (n = 50). The probability of obtaining a 6 from throwing a fair die is 1/6, and the probability of getting a “6” in one throw remains the same and is not affected by another throw.
How we define a binomial distribution
A binomial distribution is usually written in this manner:
X~ B(n, p)
X refers to the event (from the example 1 above, it refers to the number of heads obtained).
B refers to binomial distribution
n refers to the total number of independent trials in the binomial distribution
p refers to the probability of a success in each trial.
For example 1 above, we can write the binomial distribution as X~B(10, 0.5).
How to calculate the probability of the binomial distribution
For a binomial distribution, defined as X~B(n,p), the probability can be calculated using this formula:
Many scientific and graphic calculators are also able to calculate these probabilities given x, n and p. You may like to use the calculator here to calculate these probabilities.