Series or Parallel
If you have three able men, how would you handle them?
Suppose that each man has reliability in work of 100 operations at a ratio of 99%. It means each of them might make a mistake once in 100 operations at a probability of 1%.
You order them to accomplish a task needing 300 operations of any sort. But you tell each one to work for jut 100 operations. The first one does his job for 100 operations and then pass it to the next one. The second one does his job for next 100 operations to pass it to the last man.
In this case, a probability of occurrence of an error is 1 - (0.99 x 0.99 x 0.99) = 0.0297. A possibility that this task jointly tackled cannot be perfectly accomplished is 2.97%.
Now there is another group of three men whose reliability of 300 operations is 90%, 85%, and 80%, respectively. It means even the best of them might make a mistake once in 300 operations at a probability of 10%.
But, if you make them do the same task you ordered to the first group, they can do better.
You make these three mediocre men tackle the task in parallel for 300 operations for each. Each man does the whole task of 300 operations alone separately but simultaneously.
Then a probability that you cannot get a perfectly accomplished task at all from any of these three men is 0.1 x 0.15 x 0.2 = 0.003, namely 0.3%.
So, if you want one perfectly accomplished task with three men in charge, you should not have three excellent men divide the task and each of them take one third. If they work in series, relaying the task, the task will fail in a probability at about 3%.
But if you have three mediocre man get engaged each in the whole task independently or in parallel, all the tasks will fail in a probability only at about 0.3%.
In other word, we need two or more men who can work for long hours at mediocre reliability than the same number of guys who can work only for short hours even if at excellent reliability.
To make sure, of course, the former case comprises 300 operations in total, but the latter involves 900 operations in total, which is called redundancy.
**** **** ****
Gen 2:15 And the LORD God took the man, and put him into the garden of Eden to dress it and to keep it.
Gen 2:16 And the LORD God commanded the man, saying, Of every tree of the garden thou mayest freely eat:
Gen 2:17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.