Roll a die twice, P(even then odd)

Step by step

The question

Question: A die is rolled twice.

What is the probability of getting an even number, then an odd number?

1 Independent or not

The first roll does not change the second.

We call them independent.

It is the same die, with the same 6 sides.

2 Draw a tree

We want an even number, then an odd number.

That is this path, in red.

3 Multiply along the branches

And means both happen.

We multiply along the path: 3/6, times 3/6.

Careful!

And means multiply, not add.

Before we multiply, we make the numbers smaller.

3 on top and 6 at the bottom both divide by 3.

3 on top and 6 at the bottom both divide by 3.

To multiply fractions, we do top times top, and bottom times bottom.

1 times 1 is 1.

2 times 2 is 4.

So it is 1/4.

4 Check

Let's check the tree.

Each end: multiply along its branches.

We do not cancel, so every bottom is 36.

All the ends together: 9 plus 9 plus 9 plus 9 is 36.

36/36 is 1.

So the tree is right, and so is our path!

Let's look back.

First: independent or not.

Then: draw a tree.

Then: multiply along the branches.

Last: check.