Step by step
The question
Question: A bag has 4 red and 2 blue marbles.
Two marbles are picked, one after the other.
The first one is not put back.
What is the probability the second is blue, given the first is red?
The line means given.
We already know the first is red.
P stands for probability.
The line stands for given.
1 Draw a tree
2 Go along the given branch
Given the first is red: we go along the red branch only.
3 Read the next branch
From there, blue is the branch with 2/5.
So the probability is 2/5.
One red is already out of the bag.
Careful!
That is the probability of both.
Here the first is already red: we only need the second branch.
4 Check
Let's check with the rule: the probability of both, divided by the probability of the first being red.
Times 4/6, then divided by 4/6: we are back to 2/5.
The same.
So the answer is right!
Let's look back.
First: draw a tree.
Then: go along the given branch.
Then: read the next branch.
Last: check.