Question 1118550
you have 3 branches to start with.


they are A,B,C


p(A) = .5
p(B) = .3
p(C) = .2


the second trial happens after the first.


the outcomes of that trial are:


p(E) = .3
p(F) = .7


p(B) stays the same at .3


p(F and B) = p(F) * p(B) = .7 * .3 = .21


p(F given B) = p(F and B) / p(B) = .21 / .3 = .7


here's what my tree diagram looks like.


<img src = "http://theo.x10hosting.com/2018/061301.jpg" alt="$$$" >


since the events are independent, p(F and B) is equal to p(F) * P(B).


since the events are independent, p(F given B) is equal to p(F).