dick.g.forslund

2022-08-15

Dear someone,

If i choose 20 cell phone numbers randomly in a population of 37 100 000 cell phone subscribers, how large is the probability that at least two of them during two days in a row (a 48 hour period) will make a call to another person in this group of 20? The actual case involve a call and then an immeditate call back, which should mean that the two subscribers know each other: So the question can maybe be reformulated: How large is the probability in a population ot 37 100 000 that two persons in a random sample of 20 drawn from the 37 100 000 know each other?

Is this enough information to answer the question?

Best regards,

D Forslund

### Answer & Explanation

According to Dunbar average person have up to 1500 other people in their social contacts ( persons that we can "recognize"). Seems like it would be valid to assume that we'll do a callback to anyone who is known for us not only the most beloved people.

Step 1: Let's divide our 20 random people by pairs.  We'll get 190 possible pairs.

Step 2: What is the possibility that the first one in each pair knows another one? Assuming that if A-person knows B-person, so B-person knows A-person

1500 / 37 100 000 ~ 0.00004043126

Step 3: What is the chance that at least one pair would recognize each other?

0.00004043126 * 190 ~ 0.0076819394

Please note, that I made tons of assumptions, and you can change the "magic" number of social contacts (1500) in Step 2 to the one that is more intuitive for you.

Do you have a similar question?

Recalculate according to your conditions!