I assume that most of you are already familiar with how the ENIGMA machine works, that the germans used during WWII.
We now that the enigma machine has 3 scramblers with each 26 setting each. That gives us: $26 \times 26 \times 26 = 17576$
Now those 3 scramblers can be oriented in 6 different positions:
123, 132, 213, 231, 312 and 321
And at the last we have the plugboard. The number of ways of connecting, thereby swapping, six pairs of letters out of 26 is enourmus: 100,391,791,500 different orientations.
And we end up with 10,586,916,764,424,000 different starting position.
Now my question is: How can I include some probability theory to calculate the breakability of the Enigma machine?
For example: If we assume we have 100 cryptanalysts and every one are trying each of their own different starting position once every 10th second, what would be the probability that one of these 100 cryptanalyst found the correct starting position withing 24 hous
Best Answer
If there are $N$ possible settings and they try a total of $M$ different randomly-chosen settings in that time period, the probability of finding the correct setting is $M/N$.
Of course what they actually did at Bletchley Park was much cleverer than that; they were able to use various techniques to narrow down the set of possible settings to a much smaller number.