Binomial Probability Calculator.
Use the Binomial Calculator to compute individual and cumulative binomial probabilities. For help in using the calculator, read the Frequently-Asked Questions or review the Sample Problems.
To learn more about the binomial distribution, go to Stat Trek's tutorial on the binomial distribution.
Enter a value in each of the first three text boxes (the unshaded boxes). Click the Calculate button. The Calculator will compute Binomial and Cumulative Probabilities.
Frequently-Asked Questions.
Instructions: To find the answer to a frequently-asked question, simply click on the question. If none of the questions addresses your need, refer to Stat Trek's tutorial on the binomial distribution or visit the Statistics Glossary.
What is a binomial experiment?
The experiment involves repeated trials. Each trial has only two possible outcomes - a success or a failure. The probability that a particular outcome will occur on any given trial is constant. All of the trials in the experiment are independent.
A series of coin tosses is a perfect example of a binomial experiment. Suppose we toss a coin three times. Each coin flip represents a trial, so this experiment would have 3 trials. Each coin flip also has only two possible outcomes - a Head or a Tail. We could call a Head a success; and a Tail, a failure. The probability of a success on any given coin flip would be constant (i.e., 50%). And finally, the outcome on any coin flip is not affected by previous or succeeding coin flips; so the trials in the experiment are independent.
What is a binomial distribution?
A binomial distribution is a probability distribution. It refers to the probabilities associated with the number of successes in a binomial experiment.
What is the number of trials?
The number of trials refers to the number of attempts in a binomial experiment. The number of trials is equal to the number of successes plus the number of failures.
Suppose that we conduct the following binomial experiment. We flip a coin and count the number of Heads. In this experiment, Heads would be classified as success; tails, as failure. If we flip the coin 3 times, then 3 is the number of trials. If we flip it 20 times, then 20 is the number of trials.
What is the number of successes?
Each trial in a binomial experiment can have one of two outcomes. The experimenter classifies one outcome as a success; and the other, as a failure. The number of successes in a binomial experient is the number of trials that result in an outcome classified as a success.
What is the probability of success on a single trial?
In a binomial experiment, the probability of success on any individual trial is constant. For example, the probability of getting Heads on a single coin flip is always 0.50. If "getting Heads" is defined as success, the probability of success on a single trial would be 0.50.
What is the binomial probability?
A binomial probability refers to the probability of getting EXACTLY r successes in a specific number of trials. For instance, we might ask: What is the probability of getting EXACTLY 2 Heads in 3 coin tosses. That probability (0.375) would be an example of a binomial probability.
What is the cumulative binomial probability?
Cumulative binomial probability refers to the probability that the value of a binomial random variable falls within a specified range.
The probability of getting AT MOST 2 Heads in 3 coin tosses is an example of a cumulative probability. It is equal to the probability of getting 0 heads (0.125) plus the probability of getting 1 head (0.375) plus the probability of getting 2 heads (0.375). Thus, the cumulative probability of getting AT MOST 2 Heads in 3 coin tosses is equal to 0.875.
Notation associated with cumulative binomial probability is best explained through illustration. The probability of getting FEWER THAN 2 successes is indicated by P(X 2).
Sample Problems.
Suppose you binary options toss a fair coin 12 times. What is the https://Po.cash/Smart/j9IBCSAyjqdBE7 probability of getting exactly 7 binary options Heads.