I have a home that has two toilets. Whenever I flush the toilet in the master bathroom and it finishes, the toilet in the spare bathroom starts running. Any suggestions on how I can stop this problem?

When you master bath ballcock shuts off there is a slight pulse of water pressue (water hammer) that is tripping the second ballcock. I would suspect that the flapper on the second toilet is slowly leaking allowing the level to drop in the second tank. Mark the inside of the tank when it first stops filling. Check it an hour later to see if it has leaked.

At plumbing supply houses, you can get a leak detector tablet packet, usually free, and you place this tablet in the tank of the toilet. If you get colored water inside the bowl after a period of say one hour you have a leak. Of course this only will work if you do not have the blue cleaner stuff in your tank already discoloring the water. But get a packet of leak detector tablets. Insert into suspected toilet tank, do not flush the other toilet, and check for colored water in bowl. Then after one hour, flush other toilet and check for colored water in the suspected toilet bowl. If you see colored water, replace the ballcock assembly.