# Thread: What is the probability a particular sequence of 6 letters appearing in 13?

1. ## What is the probability a particular sequence of 6 letters appearing in 13?

What is the statistical probability a particular set of 6 letters appearing in a 13 alpha-numerical sequence in the case of:

http://www.newshub.co.nz/home/world/...de-bumsex.html

noting that it went out to a total of 16 million respondents only and also that the 6 sequential letters could start at any position from position 1 to position 7?

2. ## Re: What is the probability a particular sequence of 6 letters appearing in 13?

Assume that there are 13 spaces and each can have 1 of 36 independent alphanumerics. There are 36^13 possibilities = 1.17x10^20 altogether.
We are considering a 6 letter message, and ignore the very rare case of that message appearing twice.
There are 8 possible starting positions. For each there we have one message and 7 odd letters, so there are 8x36^7 cases where the message appears.
So, p = 8*x36^7/(1.17x10^20) = 3.68x10^-9. With 16x10^6 codes sent out there is about a 6% chance of this particular six letter message appearing.
With many possible messages to spark attention, it is quite likely that one will be spelled out.

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