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131 LearnersLast updated on September 2, 2025
Binomial Probability Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re cooking, tracking BMI, or planning a construction project, calculators will make your life easy. In this topic, we are going to talk about binomial probability calculators.
What is Binomial Probability Calculator?
A binomial probability calculator is a tool to determine the probability of a certain number of successes in a fixed number of trials in a binomial experiment. These experiments have two possible outcomes: success or failure. This calculator simplifies the process, making it easier and faster, thereby saving time and effort.
How to Use the Binomial Probability Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the number of trials: Input the total number of trials into the given field.
Step 2: Enter the probability of success: Input the probability of success in each trial.
Step 3: Enter the number of successes: Specify the number of successes for which you want to find the probability.
Step 4: Click on calculate: Click on the calculate button to obtain the probability result.
Step 5: View the result: The calculator will display the probability result instantly.
Understanding Binomial Probability Formula
The formula for binomial probability is given by: P(X = k) = (nCk) * (pk) * ((1-p)(n-k)) Where: n = total number of trials k = number of successes p = probability of success in a single trial (1-p) = probability of failure in a single trial nCk = combination of n items taken k at a time This formula helps calculate the probability of getting exactly k successes in n independent Bernoulli trials.
Tips and Tricks for Using the Binomial Probability Calculator
When using a binomial probability calculator, there are a few tips and tricks that can help ensure accuracy and efficiency:
Ensure the probability value is between 0 and 1.
Understand the context of the problem to accurately define success and failure.
Double-check the number of trials and number of successes.
Use a decimal precision that is suitable for your scenario to avoid rounding errors.
Consider practicing with different scenarios to get familiar with the tool.
Common Mistakes and How to Avoid Them When Using the Binomial Probability Calculator
Despite using calculators, mistakes can occur. Here are some common mistakes and how to avoid them:
Mistake 1
Entering probabilities greater than 1
Always ensure probabilities are between 0 and 1. For instance, entering a probability like 1.5 for success is incorrect and will give an erroneous result.
Mistake 2
Confusing the number of trials with the number of successes
Make sure the number of successes does not exceed the total number of trials.
For example, having 7 successes in 5 trials is not possible.
Mistake 3
Using the wrong formula for non-binomial scenarios
The binomial probability formula is specific to binomial experiments. Using it for non-binomial scenarios, such as those with more than two possible outcomes, will lead to incorrect results.
Mistake 4
Rounding too early in the calculation process
Avoid rounding intermediate results to ensure the final probability is accurate. Wait until the end to perform any rounding.
Mistake 5
Ignoring independent trials assumption
The binomial probability formula assumes trials are independent. If trials are dependent, the result may not be correct. Ensure that each trial's outcome does not affect others.
Binomial Probability Calculator Examples
Problem 1
What is the probability of getting exactly 3 heads in 5 tosses of a fair coin?
Use the binomial probability formula: P(X = 3) = (5C3) * (0.53) * ((1-0.5)(5-3))
P(X = 3) = 10 * (0.125) * (0.25) = 0.3125
Therefore, the probability is 0.3125.
Explanation
There are 10 ways to choose 3 successes out of 5 trials.
With each success having a probability of 0.5, the formula evaluates to a probability of 0.3125.
Problem 2
A basketball player hits 70% of his free throws. What is the probability he makes exactly 8 out of 10 shots?
Use the binomial probability formula: P(X = 8) = (10C8) * (0.78) * ((1-0.7)(10-8))
P(X = 8) = 45 * (0.05764801) * (0.09) ≈ 0.2335
Therefore, the probability is 0.2335.
Explanation
With 45 combinations of making 8 successful shots out of 10 and each shot having a 0.7 probability of success, the probability is approximately 0.2335.
Problem 3
What is the probability of getting at least 4 sixes in 10 rolls of a fair die?
Calculate for 4, 5, ..., 10 successes and sum them:
P(X ≥ 4) = Σ from k=4 to 10 of (10Ck) * (1/6)k * (5/6)(10-k)
After computing, the result is approximately 0.0543.
Therefore, the probability is 0.0543.
Explanation
Since there are multiple outcomes, we sum the probabilities from 4 to 10 successes, considering each success has a probability of 1/6.
Problem 4
A machine produces 95% good parts. What is the probability of producing exactly 18 good parts in a sample of 20?
Use the binomial probability formula:
P(X = 18) = (20C18) * (0.9518) * ((1-0.95)(20-18))
P(X = 18) = 190 * (0.377353) * (0.0025) ≈ 0.1804
Therefore, the probability is 0.1804.
Explanation
With 190 ways to select 18 successes out of 20 trials and each success having a probability of 0.95, the probability is approximately 0.1804.
Problem 5
In a class of 30 students, each has a 20% chance of answering a question correctly. What is the probability that exactly 5 students answer correctly?
Use the binomial probability formula:
P(X = 5) = (30C5) * (0.25) * ((1-0.2)(30-5))
P(X = 5) = 142506 * (0.00032) * (0.00317) ≈ 0.186
Therefore, the probability is 0.186.
Explanation
There are 142506 ways to choose 5 successes out of 30 trials, and each success has a 0.2 probability, resulting in a probability of approximately 0.186.
FAQs on Using the Binomial Probability Calculator
1.How do you calculate binomial probability?
2.Can the binomial probability formula be used for any type of distribution?
3.What is a binomial experiment?
4.How do I use a binomial probability calculator?
5.Is the binomial probability calculator accurate?
Glossary of Terms for the Binomial Probability Calculator
- Binomial Probability: The probability of achieving a specified number of successes in a binomial experiment.
- Combination (nCk): The number of ways to choose k successes from n trials.
- Independent Trials: Trials whose outcomes do not affect each other.
- Success Probability (p): The likelihood that a single trial results in success.
- Bernoulli Trials: Experiments with two possible outcomes—success or failure.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
