Let's see how good your language of choice is at selective randomness.
Given 4 characters,
D, or a string of 4 characters
ABCD as input, output one of the characters with the following probabilities:
Ashould have a 1/8 (12.5%) chance to be chosen
Bshould have a 3/8 (37.5%) chance to be chosen
Cshould have a 2/8 (25%) chance to be chosen
Dshould have a 2/8 (25%) chance to be chosen
This is in-line with the following Plinko machine layout:
^ ^ ^ ^ ^ ^ A B \ / ^ C D
Your answer must make a genuine attempt at respecting the probabilities described. A proper explanation of how probabilities are computed in your answer (and why they respect the specs, disregarding pseudo-randomness and big numbers problems) is sufficient.
This is code-golf so fewest bytes in each language wins!