OK, I'm gonna get nerdy on you for a minute.
The gene melanocortin-1 that causes red hair is a recessive gene, which means if a person is carrying it, it isn't physically apprent. In other words, you can't tell by looking at a person. In order for a child to have red hair, both parents have to carry this gene. I'm not sure what the exact percentages are for this gene to be passed, but generally this is how it goes:

The melanocortin-1 gene in this example would be represented by "a". Notice both parents at the top are Aa, meaning they both carry it but none have red hair.
If you look at the next line (and dont think about incestuous behaviour, b/c this is purely for example)... if both parents were like the person on the far left, the AA type, the child would also be an AA type since there is no "a" to be passed on, and therefore would not have red hair. On the other extreme, if both parents were like the person on the far right, the aa type, the child would most definitely have red hair, since both parents carry the gen, and they have red hair.
That's about my extent of knowledge on this subject. If anyone has anything to add or corrections, feel free.