We have an open ground system - house built in 1960. One of the bedrooms has two prong outlets and another has mostly two prongs with a single three prong. The three bedrooms and a half bath are on the same circuit, with a working GFCI outlet in the half bath between bedroom #1 and bedrooms 2 & 3.\

We would like to switch out the two prong outlets for three prong in the two bedrooms. An electrician friend told me that installing a GFCI outlet to the first outlet in the line should protect all outlets downstream (they would need to be labeled as protected by the GFCI), but my question is would the same apply to the outlets downstream of the current GFCI?

Thanks!