It came as a shock to me to hear that all rainbows are not the usual kaleidoscope of colors. There are different kinds of rainbows, including some that are almost all red. They are rare, but they can be found.
Basically, red rainbows happen when the sun is on the horizon. When the sun is really low, the blue and green components of its light get weakened by scattering during the long journey through Earth’s atmosphere. The red light travels through more directly. This is the same reason a sunset or sunrise can look red.
Nothing in this world is really simple!
There is a really good explanation at http://earthsky.org/earth/what-makes-a-red-rainbow.
Also, Wikipedia has a good entry on the different variations of rainbows at https://en.wikipedia.org/wiki/Rainbow