A box contains 2 red balls, 3 black balls and 5 white balls, which are all the same size.

Let's now focus on the experiment of selecting a ball form the box without looking.

a) Work out the probability of the following events occurring:

-Selecting a red ball
-Selecting a black ball
-Selecting a ball which is not white

b) How do the three probabilities that you worked out above relate to each other?

Select any ball from the box in this window by dragging it with the mouse.

c) Work out the probability of each of the following events occurring:

-Selecting a ball which is not black
-Selecting a ball which is not red

d) Imagine that now we have a box which contains different coloured balls (red, black and white) which are all the same size. However, this time we don't know how many balls there are of each colour or in total. Nevertheless, you are told the following probabilities:

How much do the three probabilities add up to?
Why is this?

e) Work out the probability of the following events occurring:

• Selecting a red or black ball.
• Selecting a red or white ball.
• Selecting a black or white ball.

The probability of either A or B occurring is equal to the sum of the probability of each of them occurring:

However, this is only really true when A and B are mutually exclusive.

In the following window you can see a roulette board divided into 5 sections: three white and two red. Whenever we click on the blue "Spin" arrow the roulette spins round till the arrow on the board stops in a different section.

a) Work out the probability of:

- the arrow stopping in a red section
- the arrow stopping in a white section.

b) Spin the roulette twice. How many different outcomes are possible?

We are going to analyse the question above in more detail using the table below. The rows indicate the outcome of the first spin and the columns the outcome of the second.

	1	2	3	4	5
1	RR	RB	RR	RB	RB
2	BR	BB
3
4
5

Copy and complete the table in your exercise book and answer the following questions.

-  How many possible outcomes are there altogether?
-  How many outcomes involve the arrow stopping in both a red and white section?

c) Work out the probability of the following events occurring:

- After both spins the arrow stops in a red section
- After both spins the arrow stops in a white section
- The arrow stops in a red section after the first spin and in a white after the second
- The arrow stops in a white section after the first spin and in a red after the second
- The arrow stops in a red section and a white one.

d) What relation is there between the probabilities in sections a) and c)?

In order to look at the probabilities carefully it is a good idea to draw up a table of results like this one below:

1st spin		2nd spin
p(R)	p(B)	p(RR)	p(BB)	p(RB)	p(BR)

The probability of A and B happening at the same time is equal to the product of the probabilities of each event occurring separately:

In reality, this is only true if events A and B are independent, which is another concept you will be studying in a different unit.