If a mother has a blood type ab+- and her father has a blood type b- and she marries a man with o- blood type. what is the percent chance their son will be b- blood type?

Genetics, blood type gene has two alleles, each allele has genotype A, B or O. The A and B are dominant, and O is recessive. So allele A combined with allele O is type A. Similarly, BO is type B, AA is type A, BB is type B, OO is type O, and AB is typeAB.

If both parents have type A blood, then the alleles could be AA or AO, thus the allele A frequency is 75%, allele O frequency is 25% for both parents. 
So the chance of alleles OO is 25% × 25% = 6.25%, 
alleles AA is 75% × 75% = 56.25%, 
alleles AO is 75% × 25% = 18.75%, 
alleles OA is 25% × 75% = 18.75%.
Since AA, AO and OA are blood type A, and OO is blood type O, thus their child has 6.25% chance to be blood type O and 93.75% chance to be blood type A. 

The +/- is called the rhesus factor, with + being dominant, and - being recessive.
So if both parents are -, the kids are always -, otherwise the kids might be + or -. 

Child Blood Type Estimate Table:
Father's Blood TypeABABOMother's
Blood
TypeAA/OA/B/AB/OA/B/ABA/OBA/B/AB/OB/OA/B/ABB/OABA/B/ABA/B/ABA/B/