At the risk of being pedantic, Ali's original post asked "what are the odds". Bit difficult to answer statistically, as there are all sorts of variables. Most relevent would be the dates that both brothers joined up.
Assuming both were in service on the first day of war, then the first brother could have died on any subsequent day of the war. I can't remember exactly how many days it lasted, but it's around 1550. Therefore, the odds of brother number one being killed on any given day is 1:1449.
The odds of brother number two being killed on any single day is also 1:1449.
To work out the odds of both being killed on the same day the calculation is 1449 x 1449 = 2,099,601 to 1.
It's the same mathematical basis that also means that one set of picked lottery numbers is just as likely to win as any other set - which is why many thousands of UK punters pick 1, 2, 3, 4, 5, 6.
The frequency with which Pals have reported the occurance shows that it is much more frequent than statistics would suggest. This is, no doubt, accounted for by brothers joining together and being in action together. I havnt come across any confirmed brothers in my research but there's probably a story to be told about two members of "A" Coy, 17th Manchesters, KIA on 1 July 1916. George Smith, 8866, was the son of Charles and Emma of Lower Broughton, Salford. John Smith, 8867, was the son of Charles and Mary of Pendlebury, Salford.
I think I may have liked to have met Charles.