General question: given a series of n random numbers, of 6 digits each, what is the probability that two of those numbers have the same final 4 digits (in the same order)?
This question is from a real case scenario, taken from the Laser dinghy races.
Laser sailboats (now ILCA) have a 6 digits hull number, which is replicated onto their sails (so-called: sail number).
The final four digits are of black color, while the initial two digits are either red or blue. Here is an example:
ILCA/Laser races are usually very crowded. It is not uncommon to have more than 200 boats racing.
In most cases, there are two or more Race Officials (ROs) who take note of the finish order. (GPS trackers are not accurate enough... yet.)
Taking note of such a large quantity of 6 digits numbers is almost impossible, especially in severe weather conditions.
Therefore, usually, ROs take note of the final four digits only (i.e.: of the black numbers only).
But sometimes their duty is complicated by the fact that two different boats, with different sail numbers, share the same identical final four digits of their respective sail number. (Example: 170695 and 210695, both are 0695.)
I was wondering, what is the probability that in a fleet of 200 boats, two of them have the same final four digits?
And what is the probability that three of them have the same final four digits?
Is it relevant that in present days the sail numbers are concentrated within the range from 195000 to 221000, with a peak of boats with sail numbers between 213000 and 218000?
Somebody told me: "you shouldn't care... after all the probability is only 1 over 10000".
It looks to me like a gross mistake.
Isn't this problem similar to the "Birthday Paradox"? If yes, how can we translate the relevant formulas of that paradox to this specific case?
Thank you indeed.
D
This question is from a real case scenario, taken from the Laser dinghy races.
Laser sailboats (now ILCA) have a 6 digits hull number, which is replicated onto their sails (so-called: sail number).
The final four digits are of black color, while the initial two digits are either red or blue. Here is an example:
ILCA/Laser races are usually very crowded. It is not uncommon to have more than 200 boats racing.
In most cases, there are two or more Race Officials (ROs) who take note of the finish order. (GPS trackers are not accurate enough... yet.)
Taking note of such a large quantity of 6 digits numbers is almost impossible, especially in severe weather conditions.
Therefore, usually, ROs take note of the final four digits only (i.e.: of the black numbers only).
But sometimes their duty is complicated by the fact that two different boats, with different sail numbers, share the same identical final four digits of their respective sail number. (Example: 170695 and 210695, both are 0695.)
I was wondering, what is the probability that in a fleet of 200 boats, two of them have the same final four digits?
And what is the probability that three of them have the same final four digits?
Is it relevant that in present days the sail numbers are concentrated within the range from 195000 to 221000, with a peak of boats with sail numbers between 213000 and 218000?
Somebody told me: "you shouldn't care... after all the probability is only 1 over 10000".
It looks to me like a gross mistake.
Isn't this problem similar to the "Birthday Paradox"? If yes, how can we translate the relevant formulas of that paradox to this specific case?
Thank you indeed.
D
