09-25-2026, 05:54 PM
The RTÉ Brainstorm article explores the surprisingly small probability that a message in a bottle will both be found and be more than 100 years old. Although bottles can travel enormous distances through ocean currents, many are never found: they may drift into remote regions, break apart, become buried in sediment, or sink after filling with water. The authors, Kevin Burke and David O'Sullivan of the University of Limerick, use this real-world problem to demonstrate how elementary probability can be applied to an unusual historical question.
The first component is the probability that a bottle containing a message is found at all. The authors use an estimate of approximately 1 in 10, based on expert estimates and historical "drift bottle" experiments. Recovery rates have varied considerably by location: some historical experiments produced recovery rates such as 14% in the Gulf of Mexico, 8% in the Caribbean and 7% near northern Brazil, while a more recent Canada–Greenland experiment produced about 5%. Thus, the probability is strongly dependent on geography and ocean circulation.
The second component concerns the age of bottles that are eventually found. Using historical records of old message bottles, the authors observe that the number recovered generally decreases as age increases. They estimate the number of bottles in the 0–25-year category and obtain approximately 106 bottles in their assembled dataset, of which 12 were more than 100 years old. Consequently, the estimated conditional probability that a found bottle is at least 100 years old is approximately $12/106 \approx 1/10$.
The two probabilities can then be combined using the multiplication rule. If $P(F)$ is the probability that a bottle is found and $P(A\mid F)$ is the probability that it is over 100 years old given that it has been found, then $P(F\cap A)=P(F)P(A\mid F)$. Using the article's estimates gives $1/10\times1/10=1/100$. The authors therefore estimate roughly a 1-in-100 chance that a message bottle will both be found and be at least 100 years old. If 100,000 such bottles were floating in the oceans, about 1,000 might satisfy both conditions; under a deliberately simplified assumption that anyone among 8 billion people is equally likely to find one, an individual person's chance would be around 1 in 8 million.
Key takeaways
ARTICLE
The first component is the probability that a bottle containing a message is found at all. The authors use an estimate of approximately 1 in 10, based on expert estimates and historical "drift bottle" experiments. Recovery rates have varied considerably by location: some historical experiments produced recovery rates such as 14% in the Gulf of Mexico, 8% in the Caribbean and 7% near northern Brazil, while a more recent Canada–Greenland experiment produced about 5%. Thus, the probability is strongly dependent on geography and ocean circulation.
The second component concerns the age of bottles that are eventually found. Using historical records of old message bottles, the authors observe that the number recovered generally decreases as age increases. They estimate the number of bottles in the 0–25-year category and obtain approximately 106 bottles in their assembled dataset, of which 12 were more than 100 years old. Consequently, the estimated conditional probability that a found bottle is at least 100 years old is approximately $12/106 \approx 1/10$.
The two probabilities can then be combined using the multiplication rule. If $P(F)$ is the probability that a bottle is found and $P(A\mid F)$ is the probability that it is over 100 years old given that it has been found, then $P(F\cap A)=P(F)P(A\mid F)$. Using the article's estimates gives $1/10\times1/10=1/100$. The authors therefore estimate roughly a 1-in-100 chance that a message bottle will both be found and be at least 100 years old. If 100,000 such bottles were floating in the oceans, about 1,000 might satisfy both conditions; under a deliberately simplified assumption that anyone among 8 billion people is equally likely to find one, an individual person's chance would be around 1 in 8 million.
Key takeaways
- Multiplication rule:
$P(A\cap B)=P(A)P(B\mid A)$
- For the article's estimates:
$P(\text{found})\approx\frac{1}{10}$
- Among bottles that are found:
$P(\text{100+ years old}\mid\text{found})\approx\frac{1}{10}$
- Therefore:
$P(\text{found and 100+ years old})\approx\frac{1}{10}\times\frac{1}{10}=\frac{1}{100}$
- With 100,000 bottles:
$100,000\times\frac{1}{100}=1,000$
- With 8 billion people and equal likelihood:
$\frac{1,000}{8,000,000,000}=\frac{1}{8,000,000}$
- Important statistical caveat: these are estimates based on incomplete historical data, and the true probability depends heavily on ocean currents, geography, bottle durability, human population density and how likely people are to notice and report a bottle.
- Mathematical lesson: a complicated real-world probability can often be decomposed into simpler conditional probabilities and then recombined using the multiplication rule.
ARTICLE
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