This answer ignores the "+ve" ending of each of the specified blood types. Since you have type AB blood, you must have received a gene for type A blood from one parent and a gene for type B blood from the other parent. Since your sister has type O blood, she must have received a gene for type O blood from EACH parent. Since your dad has type B blood, (and not type AB) you must have gotten the type B gene from him. So you got your type A gene from your mother. Since each of your parents must have a gene for type O blood in order to have passed it to your sister, your mother must have type A blood.