This is an RCA WO-33A oscilliscope, from about 1960. Here's the manual (PDF), complete with a schematic.
The probe is not very capable either: one clip is for ground, one clip is 1×, and the other is 10×. The leads are very short.
The only problem with the scope was the high voltage filter cap—the big paper one in the picture below. It was leaky, both physically and electrically... it was oozing wax out the bottom and the CRT wouldn't focus.
I found a suitable (and free!) replacement cap inside an old microwave. The replacement (0.86 μF, 2000 V) is much larger than the original, so I had to install it in a different location. It's the thing wrapped in electrical tape, below.