The P traps that Dan suggested is correct, what I think he forgot to add was its not uncommon
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for these to dry up and allow the smell to enter. Also be sure that the bathroom in the basement is properly vented. Oftentimes these rooms when installed after during a renovation do not have the proper vent lines installed. When no vent or incorrectly vented drainage system is installed when large volumes of water are drained from rooms above or if the toilet in basement is flushed the suction effect that the water causes on the drain line when it empties can pull any water that is in the existing traps out resulting in the smells your experiencing.
A way to determine if your lacking in proper vents if your not sure is to flush the toilet and listen carefully to the sink drain or if you have a tub or shower its drain. If you hear a glub glub sound that is the water that the toilet flush water is trying to pull out of the traps indicating that you do not have proper venting.
A way to determine if your lacking in proper vents if your not sure is to flush the toilet and listen carefully to the sink drain or if you have a tub or shower its drain. If you hear a glub glub sound that is the water that the toilet flush water is trying to pull out of the traps indicating that you do not have proper venting.