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Many years ago, my cousin received a phone call asking him if his name was Bill Perkins (not his real name, for security reasons). He replied that it was. The caller also asked if he had a Saab automobile, which he did. The caller then asked if he had a three-legged dog, to which the answer was also yes - the dog's name was Tripod, for obvious reasons. The caller then went on to ask about the grading of an exam in his Econ course. My cousin replied that he was the wrong Bill Perkins, and that the caller must have intended to reach the other Bill Perkins, who lived a few houses down on the same street. Something to note is that there were only 41 houses on that street.
In a recent conversation with my cousin, he told me this story, and said he thought the caller's confusion was the result of an amazing coincidence. My cousin attempted to work out the odds of such a coincidence and brought this up to me due to my mathematics training.
Although my cousin had worked out some calculations that included estimates for how many Saabs there were in the country at that time, and how many three-legged dogs there might be, all I'm interested in is some guidance on how we might calculate the probability of having two men with the same first and last names living on a street with only 41 homes.
The scenario that I've laid out occurred in 1986, so the figures my cousin used were, I believe, appropriate for that time.
U. S. population in 1985: ~240,000,000
Proportion of people in US with surname "Perkins" : 0.15% (gotten from a table of most-common surnames in the US)
Approx. no. of people in US with surname "Perkins: 240,000,000 X 0.15% = 360,000
Approx. no. of males in US with surname "Perkins": 360,000 X 0.5 = 180,000
First name of Bill or William is or was very common at the time, at about 1% of boys born at this time given this name.
Approx. no of males in US with surname "Perkins" and first name William (Bill): 180,000 X 0.01 = 1,800
My cousin then made the assumption that owners of the homes on that street would be 22 years of age or older, arriving at a figure of 70% of the population in the previous paragraph.
Approx. no. of males in US named William "Perkins" of age >= 22: 1800 X .7 = 1,260
So far, so good. Where I got stumped on this problem was calculating the probability that of all of the houses/homes in the US, two men with essentially the same name happened to live in two of the 41 homes on that street.
Would the calculation involve an assumption that males with that name and age cohort be normally distributed amongst all of the homes/residences of the US? Would the calculation involve some sort of combinatorics?
My cousin did a calculation, but since it didn't involve the matter of the 41 houses on that street, I didn't take things any further. If you have some advice, it would be much appreciated.
In a recent conversation with my cousin, he told me this story, and said he thought the caller's confusion was the result of an amazing coincidence. My cousin attempted to work out the odds of such a coincidence and brought this up to me due to my mathematics training.
Although my cousin had worked out some calculations that included estimates for how many Saabs there were in the country at that time, and how many three-legged dogs there might be, all I'm interested in is some guidance on how we might calculate the probability of having two men with the same first and last names living on a street with only 41 homes.
The scenario that I've laid out occurred in 1986, so the figures my cousin used were, I believe, appropriate for that time.
U. S. population in 1985: ~240,000,000
Proportion of people in US with surname "Perkins" : 0.15% (gotten from a table of most-common surnames in the US)
Approx. no. of people in US with surname "Perkins: 240,000,000 X 0.15% = 360,000
Approx. no. of males in US with surname "Perkins": 360,000 X 0.5 = 180,000
First name of Bill or William is or was very common at the time, at about 1% of boys born at this time given this name.
Approx. no of males in US with surname "Perkins" and first name William (Bill): 180,000 X 0.01 = 1,800
My cousin then made the assumption that owners of the homes on that street would be 22 years of age or older, arriving at a figure of 70% of the population in the previous paragraph.
Approx. no. of males in US named William "Perkins" of age >= 22: 1800 X .7 = 1,260
So far, so good. Where I got stumped on this problem was calculating the probability that of all of the houses/homes in the US, two men with essentially the same name happened to live in two of the 41 homes on that street.
Would the calculation involve an assumption that males with that name and age cohort be normally distributed amongst all of the homes/residences of the US? Would the calculation involve some sort of combinatorics?
My cousin did a calculation, but since it didn't involve the matter of the 41 houses on that street, I didn't take things any further. If you have some advice, it would be much appreciated.