In addition to not knowing the total number of bottles thrown into the sea, there is still a risk that many of them will break or become trapped in sediment.
Recently, a 100-year-old found on the southwest coast of Australia. In it, a soldier from the First World War proclaimed that he was very happy.
If you like to bet, you probably I wouldn’t expect big odds of this happening. A bottle thrown into the ocean can end up anywhere.
If it floats to a remote location, there is little chance of anyone finding it by chance. And if it ends up in a more favorable place where people can potentially find it, there are other problems. The message itself will deteriorate over time, as the light degrades it. If the bottle fills with water, it will sink and will almost certainly never be found.
So what are the chances that a message in a bottle will be found and be over 100 years old? And what are your chances of finding this bottle?
Despite these many possibilities over the life of a bottle, the probability we are looking for It’s a simple calculation. Just count the number of bottles with messages found that are more than 100 years old and divide by the number of messages sent in this way (assuming you know how many were sent):
The diagram below shows a hypothetical situation in which 20 bottles are sent in total, of which six are found (indicated in gold) and one of which is over 100 years old (indicated by the “100” stamp). Therefore, one in every 20 bottles is found and is more than 100 years old. (Note: This is just a hypothetical calculation, not actual data.)
Instead of calculating the probability directly, another way to do this is by dividing the problem into two parts: (A) a bottle with a message is found and (B) the bottle found costs more than 100. These two probabilities can be calculated separately and multiplied together to get the desired result:
This is known as the “multiplication rule” of probability, and we confirm, from our hypothetical numbers, that (6/20) × (1/6) = 1/20, as before.
Both approaches to calculating this probability are simple. However, direct calculation requires know the total number of bottles sentwhich is very difficult to know in the real world.
The multiplication rule has the advantage of dividing the calculation into two parts. We can treat each one separately and then combine the two results to obtain the desired probability. This is useful in real situationswhere we can obtain information from different sources.
Firstly, let’s address the probability of a bottle with a message being found, regardless of its age.
Experts from the German Federal Maritime and Hydrographic Agency suggest one chance in 10 that a message is found in a bottle. This is largely in line with several historical “drifting bottle” experiments, in which oceanographers released large numbers of bottles to understand ocean currents.
For example, studies from the 1960s and 1970s in the North Atlantic Ocean led to 14% recovery rates in the Gulf of Mexico, 8% in the Caribbean Sea and 7% on the north coast of Brazil. A more recent study further north (between Canada and Greenland) from the 2000s led to a recovery rate of 5%.
It is expected that results will naturally vary according to different experiments carried out in different parts of the world. But for simplicity’s sake, let’s take 1 in ten as the probability of finding a bottle with a message.
Now, for the second part of the calculation: of the bottles found, What proportion is over 100 years old?
The table below summarizes data from news articles collected on Wikipedia about very old bottles with messages that have been found. However, only data was collected on bottles over 25 years oldpresumably because older bottles are more newsworthy.
Therefore, we need to estimate the number of bottles with messages aged between 0 and 25 years old.
The table shows that fewer bottles with messages are found as they age. The messages in the bottles degrade over timewhich means bottles are more likely to break and sink, or simply become covered in layers of sediment. Plotting this data on the graph below helped to visualize the trend in the ages of the bottles found more clearly.
By drawing a line to represent this trend observed in the ages of the bottles found. This red line on the graph corresponds to the equation:
This equation provides an estimate of how many bottles were found for any specific age group (where 25 = 0 to 25 years, 50 = 25 to 50 years, and so on). The focus is on bottles aged 0 to 25 years, so the equation suggests that they were 46 bottles found in this age group.
Adding this value to all the numbers in the table, we obtain a total of 106 bottles found, of which 12 are more than 100 years old, and 12/106 is approximately one in ten.
To recap the above: (A) one in ten bottles contains messages, of which (B) one in ten is more than 100 years old. Combining these results using the multiplication rule, we estimate that the probability of a message in a bottle being found and being more than 100 years old is (1/10) × (1/10) = 1/100.
So if there are 100,000 bottles with messages floating around the oceans waiting to be found, we would expect that 1000 of them were found and were 100 years old or older. Assuming that anyone in the world has the same probability of finding one of these bottles, considering the current world population of 8 billion people, this represents a chance of approximately one in 8 million of finding one – quite unlikely.
However, some people are more persistent in looking for messages in bottles than others. Following ocean currents (known as gyres) can provide clues about where to look.
Specifically, peninsulas or islands that intersect these gyres could be good places. For this reason, it has been suggested that Caribbean islands are in an ideal position to find bottles, as they are in the path of the North Atlantic Gyre. Which sounds like a great reason to travel to the Caribbean!
But let’s also think about poor soul stuck on your desert islandwho certainly won’t appreciate the low odds of your SOS being found.
