A bag has 5 red and 3 blue marbles, two are picked without… Step by Step

Step by step

The question

Question: A bag has 5 red and 3 blue marbles.

Two marbles are picked, one after the other.

The first one is not put back.

What is the probability the first is red and the second is blue?

1 Independent or not

The first marble is not put back.

1st → changes the 2nd

We call them dependent.

dependent:

the 1st changes the 2nd

So the second pick has one marble fewer: 7.

And the colour picked first has one fewer.

2nd pick = 8 − 1 = 7 marbles left

2 Draw a tree

We want red, then blue.

That is this path, in red.

3 Multiply along the branches

And means both happen.

We multiply along the path: 5/8, times 3/7.

P(red then blue) = 58 × 37

and: multiply along the branches

Careful!

The first marble is not back.

The second pick is out of 7.

Careful: not 58 × 38 ✗

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

P(red then blue) = 5 × 38 × 7

5 times 3 is 15.

8 times 7 is 56.

So it is 15/56.

P(red then blue) = 1556

4 Check

Let's check the tree.

Each end: multiply along its branches.

We do not cancel, so every bottom is 56.

All the ends together: 20 plus 15 plus 15 plus 6 is 56.

56/56 is 1.

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

2056 + 1556 + 1556 + 656 = 5656 = 1

Let's look back.

First: independent or not.

Then: draw a tree.

Then: multiply along the branches.

Last: check.

Answer