I remember a science-fictional religious order that worships Finagle and his prophet Murphy.
ETA: Niven wrote a bunch of books all set in one universe and they're referred to as the Known Space series. Ringworld was published in 1970, so that may be what your brother remembers (it was a book not just a short story--you said he remembered a paperback--and was quite popular), but there were many more stories and books in that universe, so without more details, I'm not sure how to narrow it down. One possibility is that there's a collection of several of the short stories called Tales of Known Space that was published in 1975. There's a photo of the cover at that Wikipedia page he might look at to see if it's familiar.
Within those books is a culture called the Belters, a civilization of asteroid miners that grew out of the asteroid belt of our solar system to expand into other star systems.
Belters created their own distinct culture, placing high value on independence, self-reliance, neatness, and care for one's self and machinery. Living and working in vacuo, carelessness or lack of maintenance can be deadly. Belters don't use gesture or make careless movements; in a small mining ship, one could easily hit the wrong control by mistake. They tend to be anarchic, scornful of authority, and intolerant of fools.
Here's a description of Finagle's Law and the religion centered around Finagle and Murphy within the Belter culture:
The label ‘Finagle's Law’ was popularized by SF author Larry Niven in several stories depicting a frontier culture of asteroid miners; this ‘Belter’ culture professed a religion and/or running joke involving the worship of the dread god Finagle and his mad prophet Murphy.
And in this description of the god Finagle are actual references to some story names:
A fictional deity originating in Belter culture, whose name is invoked to express frustration. "Murphy" (of "Murphy's law") is his fictional prophet. Expressions include "Finagle take my luck!", "Finagle's gonads!", "Finagle fool you all!",...
Reference: "The Soft Weapon", "Grendel", "There Is a Tide", Ringworld chs. 2-3, 5, 9, 14-17