Birthday Buddies GXWeb

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Birthday Buddies
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What is the chance of sharing a birthday with someone in your class?
Imagine people entering a room, one at a time. If you are alone in the room, then the chance of you sharing a birthday with someone else in the room is clearly 0. But what is the probability when there are others in the room?
For just two people, the problem is not very difficult, but it quickly becomes very complicated. It actually makes things easier to consider the probability that people do NOT share the same birthday!
Use the tool which follows to try out some different group sizes, and think about the results - you may well find them surprising!

And if you are interested in an algebraic model for this problem, click to view an approximation.

Can you find a better model?

\(x = \)

0 15 100

\(f(x)\)

\(g(x)\)

\(h(x)\)

App generated by GXWeb

In a group of size 15 the chance of two people sharing the same birthday is \[25.3\%\]

About

1. What is the probability of sharing a birthday when there is one other person in the room (assume it is not a leap year).

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2. What is the chance that you and one other person are NOT birthday buddies?

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3. Now a third person enters the room. You can choose any day of the year, but in order NOT to share that day, the second person must choose from 364 days, and the third person from one less. So the chance of the three of you NOT sharing a birthday will be the product of three probabilities:

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4. In the last question, part of the solution for three people involved the product 365 x 364 x 363, reducing 365 by 3. Define a function 'fact(x)' using factorials to reduce 365 by 'x': fact(x) =

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5. What then is the probability (expressed as a percentage) of you sharing a birthday with one of 'x' people: bbuds(x) =

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How difficult did you find this activity? Please assign a rating value from 1 (very easy) to 5 (extremely difficult). Comments? Suggestions? What did you learn from this activity?

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Birthday Buddies

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