This document provides examples and explanations of calculating probabilities of multiple independent events occurring. It demonstrates how to calculate the probability of two events occurring by multiplying the individual probabilities. Examples include calculating the probability of rolling certain numbers on dice and landing on certain spots on spinners or coins landing on certain sides. The document ensures understanding by providing interactive demonstrations and asking the reader to calculate probabilities of multiple events in different scenarios.

1. Probability – Mutliple Event – Demonstration
This resource provides animated demonstrations of the mathematical method.
Check animations and delete slides not needed for your class.

2. Sal & Sara both have a bag with cubes in.
Sal picks a cube randomly, then Sara picks a cube randomly.
What is the probability that a red & a yellow cube are picked?
1
4
There is one way to get a red & a yellow cube.
To help, we can list the possible outcomes.
There are 4 possible outcomes.
P(red & yellow) =
What is the connection between
the individual probabilities & the combined probability?

3. Sal & Sara both have a bag with cubes in.
Sal picks a cube randomly, then Sara picks a cube randomly.
What is the probability that a red & a yellow cube are picked?
1
6
There is one way to get a red & a yellow cube.
To help, we can list the possible outcomes.
There are 6 possible outcomes.
P(red & yellow) =
What is the connection between
the individual probabilities & the combined probability?

4. Sal & Sara both have a bag with cubes in.
Sal picks a cube randomly, then Sara picks a cube randomly.
What is the probability that a red & a yellow cube are picked?
1
9
There is one way to get a red & a yellow cube.
To help, we can list the possible outcomes.
There are 9 possible outcomes.
P(red & yellow) =
What is the connection between
the individual probabilities & the combined probability?

5. To find the probability of two events happening,
we multiply their probabilities together.
If we pick a cube from the first bag,
then pick a cube from the second bag:
p(red & yellow) = p(red) p(yellow)
×
1
3
1
3
1
9
× =
=
=
=
=
=
=
=
=
=
We can show this with
a tree diagram.
There are 9
equally likely outcomes.

6. p(red & yellow) = p(red) p(yellow)
×
1
3
1
4
1
12
× =
=
There are 12
equally likely outcomes.
=
=
=
=
=
=
=
=
=
=
=

7. Mike & Mitch both have a coin.
Mike flips his coin, then Mitch flips his coin.
What is the probability both are tails?
Tails Heads
Tails TT TH
Heads HT HH
Sample Space Diagram
Tree Diagram
Tails
Heads
Tails
Heads
Tails
Heads
1
2
×
1
2
=
1
4
P (TT) =

8. Find the probability of these combined events.
1 cube taken from each bag.
P (red & yellow cube) =
1 cube taken from each bag.
P (red & yellow cube) =
1 cube taken from each bag.
P (red & yellow cube) =
1 cube taken from each bag.
P (red & yellow cube) =
1
2
×
1
2
=
1
4
1
3
×
1
2
=
1
6
1
2
×
2
3
=
2
6
=
1
3
2
3
×
3
4
=
6
12
=
1
2

9. Mike rolls a dice & flips a coin.
DEMO
What is the probability the dice lands on 6
AND the coin shows tails?
P(6) P(Tails)
1
3
1
3
=
1
9
×
Probability of Combined Events

10. Zoe spins the spinner twice.
DEMO YOUR TURN
What is the probability it lands on 4 twice?
P(4) P(4)
1
4
1
4
=
1
16
×
Probability of Combined Events

11. Jess rolls a dice & flips a coin.
DEMO
What is the probability the dice shows 8
AND the coin shows tails?
P(8) P(Tails)
1
8
1
2
=
1
16
×
Probability of Combined Events

12. Jess rolls a dice & flips a coin.
DEMO YOUR TURN
What is the probability the dice shows 8
AND the coin shows tails?
P(8) P(Tails)
1
8
1
2
=
1
16
×
Joe rolls a dice & flips a coin.
What is the probability the dice shows 4
AND the coin shows tails?
P(4) P(Tails)
1
4
1
2
=
1
8
×
Probability of Combined Events

13. Jess rolls a dice & flips a coin.
DEMO YOUR TURN
What is the probability the dice shows 8
AND the coin shows tails?
P(8) P(Tails)
1
8
1
2
=
1
16
×
Tom rolls a dice & spins a spinner.
What is the probability the dice shows 1
AND the spinner shows 4?
P(1) P(4)
1
6
1
4
=
1
24
×
Probability of Combined Events

14. Jess rolls a dice & flips a coin.
DEMO YOUR TURN
What is the probability the dice shows 8
AND the coin shows tails?
P(8) P(Tails)
1
8
1
2
=
1
16
×
Mo spins two spinners.
What is the probability the 1st shows 5
AND the 2nd shows 3?
P(5) P(3)
1
5
1
4
=
1
20
×
Probability of Combined Events

15. Jess rolls a dice & flips a coin.
DEMO YOUR TURN
What is the probability the dice shows 8
AND the coin shows tails?
P(8) P(Tails)
1
8
1
2
=
1
16
×
Sal spins two spinners.
What is the probability the 1st
shows an odd number
AND the 2nd shows a 4?
P(odd) P(4)
3
5
1
4
=
3
20
×
Probability of Combined Events

16. Probability of Combined Events
Jess rolls a dice & flips a coin.
DEMO YOUR TURN
What is the probability the dice shows 8
AND the coin shows tails?
P(8) P(Tails)
1
8
1
2
=
1
16
×
Kris spins a spinner twice.
What is the probability the 1st result
is odd AND the 2nd result is even?
P(odd) P(even)
3
5
2
5
=
6
25
×

17. Probability of Combined Events
Jess rolls a dice & flips a coin.
DEMO YOUR TURN
What is the probability the dice shows 8
AND the coin shows tails?
P(8) P(Tails)
1
8
1
2
=
1
16
×
Steve flips a coin three times.
What is the probability of 3 tails in a row?
P(T) P(T)
1
2
1
2
=
1
8
×
P(T)
1
2
×

18. Probability of Combined Events
Jess rolls a dice & flips a coin.
DEMO YOUR TURN
What is the probability the dice shows 8
AND the coin shows tails?
P(8) P(Tails)
1
8
1
2
=
1
16
×
Derek spins a spinner three times.
What is the probability of scoring 15 in total?
P(5) P(5)
1
5
1
5
=
1
125
×
P(5)
1
5
×

19. What is the probability of scoring
two 8s in a row on this dice? What is the probability
of scoring
two 5s in a row
with this spinner?
What is the probability of getting
four tails in a row?
What is the probability of scoring 9 in total
with these two spinners?
A cube is taken from each bag.
What is the probability they are both blue? Two cubes are taken from
this bag,
what is the probability
they are both red?
1
8
×
1
8
=
1
64
1
2
×
1
2
×
1
2
×
1
2
=
1
16
1
5
×
1
5
=
1
25
1
5
×
1
4
=
1
20
2
3
×
2
3
=
4
9
3
5
×
2
4
=
6
20
=
3
10

20. What is the probability of scoring
three 2s in a row on this dice?
What is the probability of
getting three
prime numbers
in a row?
A cube is taken from each bag.
What is the probability they are both blue?
Two cubes are taken from
this bag,
what is the probability
they are both yellow?
What is the probability of scoring
11 in total with these two spinners?
A cube is taken from each bag.
What is the probability they are all blue?
1
4
×
1
4
×
1
4
=
1
64
1
6
×
1
5
=
1
30
1
2
×
1
2
×
1
2
=
1
8
3
4
×
1
2
=
3
8
2
3
×
1
2
×
3
4
=
6
24
=
1
4
2
5
×
1
4
=
2
20
=
1
10

21. Questions?
Comments?
Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to email:
tom@goteachmaths.co.uk