Question 1026168
We have to find P(G1|R2) = P(G1 ∩ R2)/P(R2).

By the law of total probability,
P(R2) = P(G1 ∩ R2)+P(R1 ∩ R2) = P(R2|G1)P(G1) + P(R2|R1)P(R1) 

={{{(7/10)*(5/11) + (3/10)*(2/11) = 35/110 + 6/110 = 41/110}}}

==>P(G1|R2) = P(G1 ∩ R2)/P(R2) = {{{(35/110)/(41/110) = 35/41}}}.