Thursday, March 6, 2008

Birthday Paradox And Risk Evaluation


Take any random pair of people and the probability of them having the exact same birthday sits at (1/365)0.0027 or roughly 0.27%. The chance of it seems so low that many would ignore and assume it never occurring.

The Birthday Paradox however makes available mathematical means to display that the “improbable” occurs quite more often than general belief. How many people does it take to have over 50% chance of a pair sharing the same birthday?

23

Explanation, please keep in mind this example ignores leap years.

1) With 23 people 253 possible pairs exist.

23*22/2=253

(Look up Permutations if you don’t understand this)

2) Now instead of finding the chance of two people having the same birthday, let us find the probability of them having DIFFERENT birthdays.

1-1/3650.9973 or 99.73% or 364/365 in fraction

3) Plugging in the number of possible pairs.

(364/365)^2530.4995 or 49.95% chance of having every possible pair within the group to have DIFFERENT birthdays.

4) Therefore, this concludes that out of a group of 23 people, there exists 50.05% probability of having a pair born on the same date.

As shown, it takes only 23 unique people or events for something formally considered “highly unlikely” to transpire. This suggests that business operators could adopt a more meticulous and mathematical approach to risk management.

Killer storms or typhoons come on the ocean infrequently. Yet, shipbuilders make certain to construct and design the vessels to endure the worst of conditions. When it comes down to life or death, survival relies on weathering the rare catastrophes.

Does your business model include contingency plans for short term negative outcomes or if competitors employ unforeseen strategies? The investors of bankrupt New Zealand financing companies had to learn this the hard way, with some losing a lifetime of savings. I often hear the phrase “take calculated risks”, yet not many people understand the calculation part. It certainly does not equate to guessing and hoping for the best.

I plan to discuss risk management in the near future. In the mean time, free resources are available everywhere at the library or over the internet. Learn to survive the worst of times, and everything will turn out A O K.

6 Reflections:

Chris said...

I'm going to use this for work man. I like the other blogs you did better.

Rocko said...

Thank you for the feedback, Chris. What can I do to make this one as interesting as the other blogs in the past?

-Rocko

Chris said...

the novella was good. brought back good memories.

Rocko said...

You really enjoyed the series? I will think about doing it again then.

thanks again,
-Rocko

Vince said...

Take any random pair of people and the probability of them having the exact same birthday sits at (1/365)≈0.0027 or roughly 0.27%.

Sorry, this is incorrect. A dutch research revealed that the way people have sex is in a sinus-wave, not a linear or straight line. The chance people have sexual intercourse in the winter is slightly higher than the chance people have sex in the summer. There are more children born in the winter then in the summer (9 months of pregnancy).

Besides that, a year is not 365 days, but 365,2421875 days ;-)

Rocko said...

yes I'm aware that real life stats don't fit in a normal distribution. Very nice of you to mention that, I will write about it in the future!

thanks Vince