Light is additive in nature: that is, to arrive at white light, you must add red, green and blue light. That is why all the pixels in an LED videoboard are comprised of red, blue and green phosphors. It also explains how a prism is able to 'split' white light into its constituent components, which all 'add up' to white light.
Paints and pigments, however, are subtractive in nature. To get white pigment, you must subtract out all other colors. If you began with black and were able to subtract out the red and the blue, you would end up with yellow. (By the way, the only reason you have found that red + yellow + blue = muddy dark brown is because the pigments you have used are not purely balanced and differentiated. Try the same trick with some precisely varied watercolor tints of red, yellow and blue, and you'll get black. I often do it in my paintings.) The experiments of purple — red = blue, green — yellow = blue, and orange — yellow = red also illustrate that paints and pigments are subtractive.