Not homework, just a simple math problem...

[spacepirate2000]

Ok hello this is my first post. IDK how to solve this and a pay site slammed my debit card $46 without answering anything. Help? I never took probability and statistics in school.

1. Assume 333-million population of USA in 2022

2. Assume 3,780,000 surnames in USA

3. Assume 1,507,690 first names in USA

4. Assume 2.68% of the population are twins

5. Assume 0.004% are identical twins

6. Assume the odds of 2 unrelated random people appearing "identical" is 1 in 1-billion

Q: What are the odds that 2 random people have same surname?

Q: What are the odds that 6 random people have same surname?

Q: What are the odds that 2 have same first name as well?

Q: What are the odds 2 are identical twins?

Q: What are the odds that the original 6 people work in same office together?

Q: What are the odds that 6 people working in the same office have 4 "identical" unrelated Dopplegangers with same surname at same age? 2 have same first name and surname as well. 2 are identical twins.

TY

 

[mmm4444bot]

Hello spacepirate2000. We understand that these questions are not schoolwork and that you're interested in answers only. Please be patient, as it may take some time for one or more interested members to cover all of the questions. Thank you!

 

[spacepirate2000]

NP TY

 

[Dr.Peterson]

I'll give the first question a try:

1. Assume 333-million population of USA in 2022

2. Assume 3,780,000 surnames in USA

Q: What are the odds that 2 random people have same surname?

Imagine picking the first person randomly. It doesn't matter who is picked.

Now pick a second person. There are (almost) 333 million people you might choose. But how can we decide how many of them have the same surname as our first person?

If we suppose that each of the 3,780,000 distinct surnames (how would you find that number?) belong to the same number of people, which is very unlikely, then each would belong to 333,000,000/3,780,000 = 88 people. So 87 out of 333,000,000 other people have the same surname; which is a probability of 87/333,000,000 = 2.6*10^-7 = 0.00000026.

But my assumption of uniformity is not valid; what happens if the distribution is not uniform?

To consider an extreme case, suppose instead that 330 million people are all named Smith, and the other 3 million have one-of-a-kind names. Then of the 333,000,000^2/2 = 55.44 quadrillion pairs of people, 330,000,000^2/2 = 54.45 quadrillion pairs would have the same last name, so the probability of having the same last name would be 54.45/55.44 = 98.2%. This shows that the answer depends on the distribution of names; so I am not at all confident of my answer. I'd want to think a lot more about it, to see whether a realistic assumption could lead to a reasonable guess.

I should ask one thing about the overall project:

Q: What are the odds that 6 people working in the same office have 4 "identical" unrelated Dopplegangers with same surname at same age? 2 have same first name and surname as well. 2 are identical twins.

What do you plan to do with your answer? People sometimes ask this sort of question in order to either be amazed by how unlikely something is (that actually occurred), or to convince themselves that it did not really happen randomly. For such questions, I refer to this:

Should Rare Events Surprise Us? – The Math Doctors

www.themathdoctors.org

Bottom line: It doesn't really mean much.

 

[spacepirate2000]

TY for your reply.

I was using US Census and other official sources to get ballpark variables to start with, to speed things up.

I shall post the final project after all answers are posted. I dont want to bias the results. The answer may surpise you, or it was the only conclusion. My brain would explode if I attempted the math.