For the following question I wanted to know how to estimate the probability that I have selected from bin A. There are 10 bins, 4 are labelled A, 6 labelled B. Each bin has balls with two colors (Red/ blue). The distribution of red and blue balls in bin A is (0.3 to 0.7) The distribution of red and blue balls in bin B is (0.7 to 0.3). If you randomly draw two balls with replacement and they turn out to be red and blue what is the probability we selected from A?
I am getting (Probability selecting red from any Bin that is A/ Total probability selecting red from all bins)X (Probability selecting blue from any bin that is A/ Total probability of selecting a blue from all bins) =13.7%