Flip a coin and roll a die, P(tails and even)

Step by step

The question

Question: A coin is flipped and a die is rolled.

What is the probability of getting tails and an even number?

1 Independent or not

The coin does not change the die.

We call them independent.

The die still has 6 sides, whatever the coin shows.

2 Draw a tree

We want tails, then an even number.

That is this path, in red.

3 Multiply along the branches

And means both happen.

We multiply along the path: 1/2, times 3/6.

Careful!

And means multiply, not add.

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

1 times 3 is 3.

2 times 6 is 12.

So it is 3/12.

4 Simplify

Both 3 and 12 can be divided by 3.

That makes it simpler.

So it is 1/4.

5 Check

Let's check the tree.

Each end: multiply along its branches.

We do not cancel, so every bottom is 12.

All the ends together: 3 plus 3 plus 3 plus 3 is 12.

12/12 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.

Then: simplify.

Last: check.