# Probability of same last four digits of a telephone number

Yesterday I was talking to a girl and asked her for her phone number. Once she gave it to me we realized that we got exact same last four digits. Hence out of a 8 digit phone number the last 4 digits were same. She commented that maybe it’s a strong connection and then asked “What is the probability of that happening?”

Now, I haven’t done any maths (let alone probability) in a long time.

Can someone help me understand?

I think its $$\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10}$$, as each of the last 4 digits are unique. This translates to a $$0.01\%$$ chance.

Is this correct?

• That probability assumes that all 8 digit phone numbers are accounted for in the sample space. If you could guarantee that all numbers, from 00000000 to 99999999 are in use, then yes, your probability would be .01% since your sample space would include 100,000,000 and the numbers of the form $abcdxxxx$ are 10,000. – Eleven-Eleven Apr 17 '14 at 1:50
• @Eleven-Eleven thanks :-) I get your explanation . maybe you should have this as an answer :) – rockstar Apr 17 '14 at 1:52

Imagine I met someone new, and after we exchanged phone numbers, we noticed that they had the same first four digits. Wow! There’s only a 0.01% chance of that. What if our phone numbers had ended in $5463$ and $3645$, respectively? Wow! Those are the reverse of each other. That’s a rare coincidence. What if they were $1087$ and $9812$, which differ by exactly $8888$? Wow! That’s amazing! Maybe the eight digits of my number add up to 37, and that’s what his digits add up to. Not quite as rare, but still unusual.