birthday

# birthday - The Birthday Paradox 1 Two Birthdays the Same It...

This preview shows pages 1–2. Sign up to view the full content.

The Birthday Paradox September 18, 2003 1 Two Birthdays the Same It turns out that there is at least a 50% chance that in any random sample of 23 people, two of them will have the same birthday. By “birthday”, I mean you don’t include the year; so, an example of a birthday would be “June 11”. The reason that one uses the “paradox” to refer to this phenomenon is that it seems counterintuitive that a random sample of so few people should likely have a matching pair of birthdays. The reason that such a small number of people suFces is that there are many pairs of individuals, and so many chances for a collision of birthdays: Indeed, with 23 people, there are ( 23 2 ) = 253 pairs of individuals. Let us now prove that the probability is indeed 50%. ±irst, let the sample space S be the set of all sequences ( x 1 , ..., x 23 ), where 1 x i 365. The value of x i indicates the day of the year of the i th person’s birthday. We are assuming here, for simplicity, that there are no leap years, so that each year

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

birthday - The Birthday Paradox 1 Two Birthdays the Same It...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online