High School Science Fair Project Essay

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QUESTION
The Birthday Paradox states that within a group of 23 randomly selected people there is a 50% chance that two of them will have the same birthday. If the same equation is used but the amount of people is doubled, will there be more than one pair of people with equal birthdays?

HYPOTHESIS
If the Birthday Paradox is tested with twice the people than in its original formula, the results will be true and there will be more than one date where two or more people share the same birthday.

MATERIALS
Internet accesible device (Tablet, computer)
The National Football League website
Microsoft Office Software
Procedure
Step: 1. Use the formula P(d)=[(365!/319!)/(365^46)] to find out the theoretical probability of having a match, which is a P(d) [the resulting number is a value of approximitely 0.05174716]. 2. Next use the equation P(s) = 1- P(d), and the result will be the theoretical probability of having a matching birthday in the group, which is P(s) [the resulting number is a value of approximitly 0.948]. 3. Convert the obtained value in step 2 into a percentage by multiplying the value by 100 (the percentage is a value of 95%, the probability of having one match of birthdays in each test group of 46 people.) 4. Then, using the internet, go to www.nfl.com and find five teams in the National Football League with at least 46 people. 5. Access the roster of a team and record the birthdays of 46 players on the team. 6. Repeat step four until five groups of birthdays have been collected. 7. Once the birthdays have been collected, analyze data by recording how many people have the same birthday(s) within each test group.

INTRODUCTION
Birthday’s are usually thought of as a person’s day of birth. They are pretty much that one day of the year where a person can celebrate

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