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 Paradox 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 complement probability (all birthdays being unique) and subtracts it from 1.

3. Importance of the Birthday Paradox

Details: This principle has important applications in cryptography, hashing algorithms, and understanding probability in daily life.

4. Using the Calculator

Tips: Enter the number of people in the group (1-365). The calculator will show the probability that at least two people share the same birthday.

5. Frequently Asked Questions (FAQ)

Q1: Why is it called a paradox?
A: Because the probability is much higher than most people intuitively expect for small groups.

Q2: How many people are needed for a 99% probability?
A: About 57 people give a 99% chance of a shared birthday.

Q3: Does this account for leap years?
A: No, the standard calculation ignores February 29th for simplicity.

Q4: What about uneven birthday distributions?
A: The calculation assumes birthdays are uniformly distributed throughout the year.

Q5: Can I calculate for other numbers of possibilities?
A: Yes, the general formula replaces 365 with the number of possible outcomes.