Murphy eventually

Murphy's Law says  "Anything that can go wrong will go wrong eventually".  I am sure everyone has heard of it. Guess what! Murphy was right. Here is a simple statistical trick to prove it.


Step 1
Let's say,    
Probability that A can go wrong                                      =   p
Probability that A cannot go wrong                                  =  1 - p
Probability that A has never gone wrong after n trials      = (1 - p)^n


Step 2
Probability that A will go wrong at least once after n trials
= 1 - Probability that A has never gone wrong after n trials
= 1 - (1 - p)^n

Step 3
Probability that A will go wrong eventually
= lim (n -> infinity)        Probability that A will go wrong at least once after n trials
= lim (n -> infinity)             1 - (1 - p)^n   
=              1                -       lim (n -> infinity)        (1 - p)^n 

=              1                -       0                                                             { because 0 < 1 - p < 1 }
=              1


QED. Isn't it neat?