Direct connection of scope

When can you directly connect scope probes without need of isolation transformer. I am aware that if you don't use transformer you run the risk of frying your scope. Is this only a problem when dealing with ac voltage. I asked a friend of mine this question and he said that if I wired a two prong plug ( no ground ) into a receptacle and then plugged my scope into this receptacle I could directly connect my scope probes without fear of shorting to ground. Looking for a second opinion. Thanks in advance.

The issue is caused when a direct link occurs through the scope probe ground and mains supply ground and you are connecting to equipment with a live probe point. The path is :
scope ground wire --- screen of probe cable --- oscilloscope ground --- power cord --- mains earth pin.

The problem applies to AC or DC.

If the probe point ground is already grounded or floating there is usually no problem but shorting something live to ground through that path will obviously cause problems or damage. The isolating transformer allows the scope to be powered normally but breaks the path to ground so no current can flow through it. Note that almost all scopes already have a power transformer that gives good isolation. I would advise in most cases to still make a ground connection but through a high voltage rated 1M resistor to help to stop the scope body rising to high voltages.

Brian.

Its better to use a battery operated oscilloscope