Birthday problem

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/birthday-problem

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. How big is Birthday problem?23 individuals
2. What is the number of unique pairs in a group of 23?253 pairs
3. What is the mathematical approach to probability calculation?Calculating the complement probability (probability of no match)
4. How many people do we need for a 50% chance that two share a birthday?With just 23 people, the chance that two of them have the same birthday is over 50%.
5. Why does the chance of a shared birthday increase so fast with more people?Each new person can be paired with all the people already there, so the number of possible pairs grows quickly and gives many chances for a match.

Birthday Problem: A probability theory problem concerning the likelihood of shared birthdays in a randomly selected group of individuals.
Birthday Paradox: The counterintuitive finding that only 23 people are needed for a greater than 50% probability of at least two sharing a birthday.
Probability: A numerical measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
Hash Function: A function that maps data of arbitrary size to data of a fixed size, used in cryptography and data integrity.