Coin Flip Probability Calculator with Logs

Example: Getting exactly 5 heads in 10 flips

1. Determine your experiment: We want to calculate the probability of getting exactly 5 heads when flipping a fair coin 10 times.
2. Number of flips: Set this to 10
3. Success condition: Choose "Exactly" since we want exactly 5 heads
4. Number of heads: Set this to 5
5. Probability of heads: For a fair coin, this is 0.5
6. Calculate: The result will be approximately 24.61%

Formula Explanation

The binomial probability formula used is:

P(X = k) = C(n,k) × p^k × (1-p)^(n-k)

• n: Number of trials (flips)
• k: Number of successes (heads)
• p: Probability of success on each trial
• C(n,k): Binomial coefficient "n choose k"

Supported Calculations

• Exact number of successes (exactly k heads)
• At least k successes (k or more heads)
• At most k successes (k or fewer heads)
• Fair and unfair coins (adjustable probability)
• Large number of flips (efficient calculation)

Real-World Applications

This calculator can be used for quality control testing, clinical trial analysis, survey results, sports statistics, and any scenario with binary outcomes (pass/fail, yes/no, success/failure).

For comparing age differences in groups, try our Bulk Age Difference Calculator for group statistics. For business metrics, see the Churn Rate Calculator for customer retention analysis.

Educational Value

Perfect for learning probability theory, statistics courses, understanding binomial distributions, and practicing with real examples and step-by-step explanations.

Explore more tools in our Statistics tools collection.

Privacy & Data

All calculations happen in your browser. No data is sent to servers. Your calculation history is stored locally and can be cleared anytime for complete privacy.