I work many PT positions and while I get guaranteed hours and I am paid if they don't need me, I usually take sick days off unpaid. I hardly EVER call in sick, only when I might be contagious with something non cold like where the kids might have already been exposed, or I can't stand much less be able to work.
Usually parents are pretty good about letting me do a babysitting night later on to earn the chance to get that pay that I missed out on, or will just give it to me paid anyways. Or if I am feeling just slightly under the weather and they are home and can let me go, they might offer to let me go home early with full pay. But I never expect paid sick with PT positions and I would never act like that summer sitter without mentioning how I feel to the parents and let them decide what they want to happen.
Also, as mentioned for a very short term gig like this, I would probably assume no pay and no make up hours for it.