Step by step
The question
Question: the probability of sun is 0.6.
If sun, the probability of walk is 0.8.
If no sun, it is 0.3.
Find the probability of walk.
1 Draw the tree
The branches from one point add up to 1.
So no sun is 1 minus 0.6: 0.4.
And not walk is 1 minus each: 0.2 and 0.7.
2 Multiply along the branches
Sun then walk: we multiply along the branches.
0.6 times 0.8 is 0.48.
The same for every end.
No sun then walk: 0.4 times 0.3 is 0.12.
3 Add the paths
Walk can happen two ways: after sun, or after no sun.
We add the two paths.
Careful!
Multiply along each branch first.
0.8 only counts when it is sun.
0.48 plus 0.12 is 0.6.
4 Check
Let's check: the four ends add up to 0.48 plus 0.12 plus 0.12 plus 0.28.
That is 1: every way is counted once.
So the answer is right!
Let's look back.
First: draw the tree.
Then: multiply along the branches.
Then: add the paths.
Last: check.