The timing of a cold frontal passage is coming into better focus. It appears that the front will pass through the area early Sunday morning, making it more likely that the majority of rain will pass through Mid-Ohio overnight on Saturday night, and bring dry weather behind the front on Sunday. There will still be a fairly moist and unstable air mass over Ohio on Saturday, which could lead to some scattered showers and thunderstorms around the track. But I'd put the chance of one hitting the track at 40% during the day. If a shower does pass over the track, it could produce around a tenth of an inch of rain, so not a huge amount, and it should be short-lived.
The chance of rain rises Saturday night as the front will provide additional lift for storms to develop. The front is expected to be to the east of Mid-Ohio by sunrise Sunday, and a slightly cooler and less humid air mass will build in from the northwest. Sunday should be a beautiful day for racing, with partly sunny skies and afternoon highs in the upper 70s.