In July 1951 Leo Fender was working in his Fender workshops, designing his Fender Precision Bass. This was the first ever solid body (as opposed to acoustic guitars or double basses which are hollow) electric bass. Bass players in the 30s and 40s were struggling to be heard above the rest of the band on their relatively quiet double basses, instruments borrowed from the classical orchestra. Ampeg, a company still around today, experimented with a microphone which fitted in the spike (sometimes called a peg) at the base of the instrument. This amplified peg gave Ampeg its name. This was not a very big success. When Leo made his bass, he also made the first decent bass amplifier, the Bassman. This also helped with the success of the P-bass. Fender obviously took a lot of inspiration from his Telecaster guitar, designed in the late 40s, as can be seen in the shape of the scratch-plate and the positioning of the controls.
Also, it is the 50th anniversary of the P-bass this year.