Binomial Distribution Calculator

What Is It?

A binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. This calculator helps visualize and compute:

• Probability of exactly k successes
• Cumulative probabilities
• Distribution shape and statistics

Key Formula

The probability mass function:

P(X = k) = C(n,k) × p^k × (1-p)^(n-k)

Where:

• n = number of trials
• k = number of successes
• p = probability of success
• C(n,k) = combination (n choose k)

How to Use

1. ‌Enter Parameters‌:

   • Number of trials (n)
   • Probability of success (p)

2. ‌View Results‌:

   • Interactive probability chart
   • Complete probability table
   • Distribution statistics (mean, variance)

3. ‌Interpret‌:

   • Hover chart bars for detailed probabilities
   • Use table for exact values
   • Check summary statistics

FAQs

‌Q: What’s the maximum number of trials supported?‌
A: The calculator handles up to 50 trials efficiently while maintaining accuracy.

‌Q: Can I use decimal probabilities?‌
A: Yes, enter any probability between 0 and 1 (e.g., 0.25 for 25% chance).

‌Q: How is cumulative probability calculated?‌
A: It’s the sum of probabilities for all outcomes up to and including k.

Terminology Explained

‌Trials (n)‌:
The number of independent experiments or observations.

‌Probability (p)‌:
The chance of success in a single trial (0 to 1 scale).

‌Successes (k)‌:
The specific number of positive outcomes you’re evaluating.

‌PMF‌:
Probability Mass Function - gives P(X=k).

‌CDF‌:
Cumulative Distribution Function - gives P(X≤k).

‌Expected Value‌:
The mean of the distribution (n × p).