Does the Observatory's chance to auto-observe increase as you build more of them?

Solution 1:

Each observatory increases the chance to auto-observe, but the chance will never be 100% because it diminishes after 75%.

The relevant part of the code is the following (inside calender.js):

var autoChance = this.game.bld.getEffect("starAutoSuccessChance");  //in %
            var rand = this.game.rand(100);

            if(
                (this.game.ironWill && (self.game.rand(100) <= 25)) ||
                (rand <= autoChance)
            ){  
                dojo.hitch(this, this.observeHandler)({}, true);
            }

Every observatory increases your starAutoSuccesChance with 1, so 11 in your case. However, this.game.bld.getEffect does the hyperbolic effect which makes sure the chance does not become 100%. In another answer(which deserves more upvotes imo) this is perfectly explained, so I will not do it again.

Here you also see is that the chance is compared with a random number under 100 (rand <= autoChance) so the autoChance (or starAutoSuccessChance untill 75 observatories) is indeed the percentage of auto-observes.

Solution 2:

Yes, each observatory adds 1% to the auto-observe chance for astronomical events. This will allow you to accumulate starcharts while letting the game run overnight, but don't plan on getting this chance very high with observatories; there's a lategame upgrade (SETI) that fixes your auto-observe chance at 100%, regardless of observatories.