In an A5/1 stream cipher, why do the registers have a stepping probability of 3/4 I know that the probability of each register to step is 3/4 but I have yet to find an explanation of why. Can anyone explain this to me?
In A5/1, there are three shift registers (about 20 bits each), each with a certain bit (about in the middle) controlling clocking. At each cycle, a register is shifted when its clock bit agrees with one or both of the other two clock bits.

Under the fair approximation that the clock bits are random, independent, and evenly distributed, a given register is thus shifted with odds $3\over4$ (derivation: as the odds of a coin toss matching either of two other coin tosses).