Question 1036371
Let {{{r[A]}}} be the event where the ball drawn from bag A is red, {{{g[A]}}} the event where the ball drawn from bag A is green.  we want to find {{{p(r[B])}}}, the probability that the ball drawn from bag B is red.

==> {{{p(r[B]) = p(r[A] and r[B]) + p(g[A] and r[B])}}}

=p({{{r[B]}}}|{{{r[A]}}})*p({{{r[A]}}}) + p({{{r[B]}}}|{{{g[A]}}})*p({{{g[A]}}})

=(1/6)*(3/5) + 0*(2/5) = 1/10.

Therefore, {{{p(r[B]) = 1/10}}}.

This also implies that {{{p(g[B]) = 9/10}}}.