In this problem, we are asked to find the possibility of selecting a 3-red-face die when the first three rolls all give red faces. which is to find P(3-R-F|3R) according to formula: P(3-R-F|3R)=P(3-R-F n 3R)/P(3R), P(3-R-F n 3R) is easy to find. to find P(3R), we need to calculate each cases: selected 1-R-F(one red face), 2-R-F, or 3-R-F thus, P(3R)=P(3R n 1-R-F)+P(3R n 2-R-F)+P(3R n 3-R-F) each of those are not hard to find. my final result was 3/4. Hope it is right.
