Birthday Paradox and Realistic Risk Assessment
Rocko Chen
March 21, 2008
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.
1-1/365≈0.9973 or 99.73% or 364/365 in fraction
3) Plugging in the number of possible pairs.
(364/365)^253≈0.4995 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.
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.
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.
1-1/365≈0.9973 or 99.73% or 364/365 in fraction
3) Plugging in the number of possible pairs.
(364/365)^253≈0.4995 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.
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.