Flip a coin and roll a die, P(tails and less than 3) Step by Step

Step by step

The question

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

What is the probability of getting tails and a number less than 3?

1 Independent or not

The coin does not change the die.

1st → does not change the 2nd

We call them independent.

independent:

the 1st does not change the 2nd

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

2 Draw a tree

We want tails, then a number less than 3.

That is this path, in red.

3 Multiply along the branches

And means both happen.

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

P(tails and less than 3) = 12 × 26

and: multiply along the branches

Careful!

And means multiply, not add.

Careful: not 12 + 26 ✗

Before we multiply, we make the numbers smaller.

2 on top and 2 at the bottom both divide by 2.

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

P(tails and less than 3) = 1 × 11 × 6

1 times 1 is 1.

1 times 6 is 6.

So it is 1/6.

P(tails and less than 3) = 16

4 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: 2 plus 4 plus 2 plus 4 is 12.

12/12 is 1.

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

212 + 412 + 212 + 412 = 1212 = 1

Let's look back.

First: independent or not.

Then: draw a tree.

Then: multiply along the branches.

Last: check.

Answer