Steve,
A bull(or steer, for that matter) with scurs, has inherited at least one copy of the scur gene - might have two, but expression is dominant in males, so only one is needed for him to express the trait. In this case, we'll say that since his sire is a purebred Angus bull, he's probably only got one copy - though there are some famous Angus bulls back in the herdbook that had scurs.
A female must have inherited two copies of the scur gene in order to express them. So...a cow with one copy will be 'smooth polled' - or horned, as was the case with this calf's Highland dam. If they have horns, the scur gene is masked, but it's still there, hiding in the background.
So...if you breed this polled/scurred bull to polled cows that lack the scur gene, all the heifers will be smooth polled - but half will inherit the scur gene. Half the bull/steer calves from this mating will express scurs, the other half will be smooth-polled.
But, if the polled cows you breed this bull to possess one copy of the scur gene(these cows will all be smooth-polled), then 25% of heifers may express scurs, 50% will be smooth-polled but possess a scur gene, and 25% will be smooth-polled and will not have inherited the scur gene. Bull/steer calves from this mating - 75% will potentially have scurs, 25% will be smooth polled.
Jeanne, horns are fairly simple, with Bos taurus cattle, but there is an 'African Horn Gene' that can also play into the mix when you start infusing some Bos indicus genetics; it's been so long since I had any Brahman influence in my herd, that I've forgotten the inheritance/expression pattern - but I think it's similar to scurs, with regard to gender influence on expression.