Calculate Dbinom 1 500 0.5

The dbinom function calculates the probability of exactly k successes in n independent Bernoulli trials, each with success probability p. This calculator computes the exact binomial probability for your specified parameters.

What is dbinom?

The dbinom function is a fundamental probability distribution in statistics. It answers questions like:

What is the probability of getting exactly 1 success in 500 trials with a 50% chance of success in each trial?
How likely is it to get exactly k successes in n trials with probability p?

The binomial distribution is widely used in quality control, medical testing, sports analytics, and many other fields where counting successes in repeated trials is important.

How to use this calculator

Enter the number of trials (n) - how many times you're performing the experiment
Enter the number of successes (k) - how many times you expect the event to occur
Enter the probability of success (p) - the chance of success in each individual trial
Click "Calculate" to see the probability

The calculator will show you the exact probability of getting exactly k successes in n trials with probability p.

The binomial probability formula

The probability mass function for the binomial distribution is:

P(X = k) = C(n, k) × p^k × (1-p)^(n-k) where: C(n, k) = n! / (k! × (n-k)!)

This formula calculates the probability of exactly k successes in n trials with success probability p.

The binomial distribution requires that trials are independent, have only two possible outcomes (success/failure), and have constant probability of success.

Worked example

Let's calculate the probability of getting exactly 1 success in 500 trials with a 50% chance of success in each trial:

n = 500 (number of trials)
k = 1 (number of successes)
p = 0.5 (probability of success)

Using the formula:

P(X = 1) = C(500, 1) × 0.5^1 × (1-0.5)^(500-1) = 500 × 0.5 × 0.5^499 = 500 × 0.5 × 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000