Rework problem 1 from section 34 of your text involving prob

Rework problem 1 from section 3.4 of your text, involving probabilities on a tree diagram.

Construct a copy of figure 3.14 in your text, where the first outcome is one of A and B the second outcome in each case is one of a and b. Use the following probabilities instead of those given in your text:

Pr[A] = [ 1/3]
Pr[B] = [ 2/3]
Pr[a | A] = [ 2/7]
Pr[b | A] = [ 5/7]
Pr[a | B] = [ 3/5]
Pr[b | B] = [ 2/5]

Find the following missing probabilities:

(1) Pr[B] =  

(2) Pr[b] =  

(3) Pr[b | B] =  

(4) Pr[B | b] =  

I got (1) and (3), but can\'t find the clue for 2 and 4.
Can someone post answer and process plz?

Solution

2) P(b) = 61/105
4) P(B|b) = 56/61