# Probability of having the same 3 first digits on phone PIN

#### SherlockPotato

##### New member
Hello everyone,
Some days ago I found out that me and this girl have the exact same first 3 digits on your phone PIN. That has been bugging me on how improbable that should be but since I dont have the knowledge (still in highscool, should learn probabilities next year) I need your help to know it. If you could also explain as detailed as possible how you get to the result I would appreciate it very much.
PS: The digits are in the same order, which is even more impressive.

#### mmm4444bot

##### Super Moderator
Staff member
Some days ago I found out that me and this girl have the exact same first 3 digits on your phone PIN.
How do you know the first three digits of my phone's PIN?

#### HallsofIvy

##### Elite Member
I presume that you mean, simply, that "this girl" has the same three digits as on your phone. If there are no special restrictions on what those digits can be ("first digit cannot be 0" for example) then there are 10 possibilities for the first digit, 10 for the second, and 10 for the third so that the probability they are each the same is 1/10= 0.1. The probability that are all three the same is (0.1)(0.1)(0.1)= 0.001. If there is the most common restriction, that the first digit cannot be 0, then there are only 9 possibilities for that digit so the probability all three are the same is (1/9)(0.1)(0.1)= 0.0011111, approximately. (Exactly 1/900).

If you really mean that both you and "this girl" have the same three digits as some third person (not mmm4444bot or me), then what ever your first digit is, the probability the two other people have the same digit is (1/10)(1/10)= 1/100 and the same for the other two digits. The probability that the other two people have the same first three digits as you is, again without restrictions on the digits, (1/100)(1/100)(1/100)= 1/1000000= 0.000001. If, again, the first digit cannot be 0, it is (1/81)(1/100)(1/100)= 1/810000= 0.000001234568.

#### SherlockPotato

##### New member
Thank you very much to both of you, I misspelled "our" for "your", it was in fact what HallsofIvy assumed.