Roll a die twice, P(odd then 6) Step by Step

Step by step

The question

Question: A die is rolled twice.

What is the probability of getting an odd number, then a 6?

1 Independent or not

The first roll does not change the second.

1st → does not change the 2nd

We call them independent.

independent:

the 1st does not change the 2nd

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

2 Draw a tree

We want an odd number, then a 6.

That is this path, in red.

3 Multiply along the branches

And means both happen.

We multiply along the path: 3/6, times 1/6.

P(odd then 6) = 36 × 16

and: multiply along the branches

Careful!

And means multiply, not add.

Careful: not 36 + 16 ✗

Before we multiply, we make the numbers smaller.

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

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

P(odd then 6) = 1 × 16 × 2

1 times 1 is 1.

6 times 2 is 12.

So it is 1/12.

P(odd then 6) = 112

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: 3 plus 15 plus 3 plus 15 is 36.

36/36 is 1.

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

336 + 1536 + 336 + 1536 = 3636 = 1

Let's look back.

First: independent or not.

Then: draw a tree.

Then: multiply along the branches.

Last: check.

Answer