Using a tree diagram for conditional probability calculations

[chwala]

Homework Statement

See attached

Relevant Equations

Probability

I would like to know how one can use the tree diagram...hence my post... otherwise, i was able to solve problem as follows,

a. $P(A∩B)= \dfrac{3}{4} ×\dfrac{1}{5}=\dfrac{3}{20}$

b. $P(B/A')=\dfrac{P(B)-\dfrac{3}{20}}{P(A')}$

$\dfrac{3}{7}=\dfrac{P(B)-\dfrac{3}{20}}{\dfrac{1}{4}}$

...

$P(B)=\dfrac{9}{35}$

c. $P(A/B)=\dfrac{3}{20} ×\dfrac{35}{9}=\dfrac{7}{12}$

 

[haruspex]

Homework Statement:: See attached
Relevant Equations:: Probability

View attachment 323090

I would like to know how one can use the tree diagram...hence my post... otherwise, i was able to solve problem as follows,

a. $P(A∩B)= \dfrac{3}{4} ×\dfrac{1}{5}=\dfrac{3}{20}$

b. $P(B/A')=\dfrac{P(B)-\dfrac{3}{20}}{P(A')}$

$\dfrac{3}{7}=\dfrac{P(B)-\dfrac{3}{20}}{\dfrac{1}{4}}$

...

$P(B)=\dfrac{9}{35}$

c. $P(A/B)=\dfrac{3}{20} ×\dfrac{35}{9}=\dfrac{7}{12}$

See Conditional Probability Tree at https://www.cuemath.com/data/probability-tree-diagram/