1. What is the Birthday Paradox?

The Birthday Paradox demonstrates that in a group of just 23 people, there's a 50% chance that two people share the same birthday. This seems counterintuitive, hence the term "paradox."

2. How Does the Calculator Work?

The calculator uses the birthday probability formula:

Where:

• \( P \) — Probability of at least one shared birthday
• \( n \) — Number of people in the group
• \( 365 \) — Number of possible birthdays (ignoring leap years)

Explanation: The formula calculates the probability that all birthdays are unique and subtracts this from 1 to get the probability of at least one shared birthday.

3. Understanding the Results

Details: The results show the probability that at least two people in your group share the same birthday. For example, with 23 people there's a 50.7% chance, and with 70 people the probability exceeds 99.9%.

4. Using the Calculator

Tips: Simply enter the number of people in your group (between 1 and 365). The calculator will show the probability that at least two people share a birthday.

5. Frequently Asked Questions (FAQ)

Q1: Why is this called a paradox?
A: It's called a paradox because the probability is much higher than most people intuitively expect for small groups.

Q2: Does this account for leap years?
A: No, this calculation assumes 365 days per year. Leap day birthdays are excluded for simplicity.

Q3: What about real-world birthday distributions?
A: This assumes uniform distribution of birthdays. In reality, some dates are more common, which slightly increases probabilities.

Q4: How accurate is this calculator?
A: Very accurate for the mathematical model described. It uses logarithms to handle the large factorial calculations precisely.

Q5: What's the minimum group size for 100% probability?
A: With 366 people (by pigeonhole principle), the probability becomes 100%. The calculator shows 99.999999% at 365 people.