Is my mom ok?

About three weeks to a month ago, my mom had knee surgery done. They replaced her knees. They had to give her a blood transfusion because she lost alot of blood. She is at home with us and is doing well. But, I was wondering, is it likly the blood they gave her has HIV/AIDS? She said it had been scaned sevral times, BUT, HIV/AIDS takes 3 weeks to 6 months for it too show up in a blood test. What if the blood had just been taken out of someone and than scaned and put in her? If they put it in her like 5 hours after taking it out from the donnor, there could be HIV/AIDS that hasn�t had enough time to show up? Is it likly they waited 3 to six months before giving it too her????