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Oh yes - and @anyone (LOL) - it is probably best to avoid the temptation, especially at the frog-end to "pull" the broken hair out. That would probably be OK now and then - but - once more and more hairs break (which they do depending on a lot of things) - the more hairs you pull-out from the ferrule/clamp on the frog - you can run the risk of loosening the hold on the remaining hairs.
Maybe not all bows / frog-ferrules are as susceptible to this - may depend on the overall construction quality - but - in summary - better, as @damfino says - to just "trim" it.
I had ( well, still have, but rarely used ) a cheap bow that came with my cheap EV - alarmingly - a few - maybe half a dozen hairs came loose - they weren't broken - just slipped from the ferrule - and as I inspected it and played about with it - a few more came out - and I was half expecting the rest to come with it. Fortunately, they didn't, but it served as a warning.....
I seriously recommend not copying my mistakes. D'oh -
Please make your own, different mistakes, and help us all learn :-)
Broken bow hairs ? The only broken hairs I've had on any of my 7 were the three bow's I've gotten from the "Fiddlershop", but only one or two were broken when I took them out of the shipping tube's. Since then not one hair has broken on any of the three.
Much of the problem with broken hairs has to do with the person (s) who hair's or re-hairs the bow. I've also had 3 re-haired by my luther and never had even one hair break or come out at the ends.