A bitstring x in $\{0,1\}^5$

is stored in vulnerable memory, subject to corruption $$ for

example, on a spacecraft. An $\backslash$alpha $-$ray strikes the memory and resets one bit to a random

value $($both the new value and which bit is affected are chosen uniformly at random$).$

A second $\backslash$alpha $-$ray strikes the memory and resets one bit $($again chosen uniformly at

random$).$ What is the probability that the resulting bitstring is identical to x$?$