1. Mutually Exclusive Events
What does ‘Mutually Exclusive’ mean?
Ask pupils for their own example of a mutually exclusive event
Ask pupils for an example of events that aren’t mutually exclusive.. Eg drawing a king and a heart from a deck of cards
For example, turning left and turning right at the same time.
Or going to Liverpool at 9am tomorrow, and going to Manchester at 9am tomorrow
Drawing an ace and a king from a deck

2. When events have no outcomes in common they are mutually exclusive.
P(A  B) = 0
E.G. Getting a 2 or a 3 in one roll of a dice. A B S 1 6 1 6 4 6

3. When deciding if 2 events are mutually exclusive ask yourself the question:
Can these events happen at the same time?

4. Mutually Exclusive Events Which of the following are mutually exclusive events?
(a) A thumb tack falling head down and a thumb tack falling head up.
(b) A student studying Maths and Physics.
(c) Getting both a head and a tail when tossing a coin.
(d) Getting a six and a two when throwing a dice.
(e) Getting a king and a club when picking a card from a pack of playing cards.

5. Winning a football matchQ1
Winning a football match
AND
Loosing the same football match

6. Q2
Getting the bus
AND
Missing the bus

7. Watching an Romance DVDQ3
Watching a comedy DVD
AND
Watching an Romance DVD

8. Q4
Being asleep
AND
Being awake

9. Rolling a number less than 3Q5
Rolling a 2
AND
Rolling a number less than 3

10. A traffic light being redQ6
A traffic light being red
AND
The traffic light being green

11. The same baby being a girlQ8
A baby being a boy
AND
The same baby being a girl

12. Randomly picking a dog from the poundQ9
AND
The dog being Black

13. Me not winning the lottery
Q10
AND
My Friend not winning the lottery

14. We use the addition rule for ‘or’ and ‘union’ questions probabilities
P(AB) = P(A) + P(B) - P(A  B)
With all these questions it is good practice to draw a Venn diagram

15. Using the addition Rule
A and B are 2 events such that P(A) = 0.8 and the P(B) = 0.5
where P(A n B) is 0.3.
Find P(A U B)
Are A and B mutually exclusive? Explain your answer.

16. Question
If A and B are mutually exclusive events where P(A) = 0.4 and P(B) = Find P(A U B)

17. Question A card is drawn from a deck of 52 cards.
What is the probability that the card is a red card or a queen?
What is the probability that the card is a club or a king?

18. Independent Events

19. When 2 events have no effect on each other they are called independent events.
Examples of Independent events
Getting a 5 on a spinner numbered 1,2,3,4,5,5,7,8 and a 3 on a fair unbiased dice.
Flipping a coin and rolling a dice
Spinning a spinner and Rolling a dice A B

20. Hint:
If it is replaced then it is independent (No effect Probabilities remain the same)
If it is not replaced then it is not independent.

21. Example A box contains 2 red counters and 4 yellow counters.
One counter is picked at random and is not replaced
What is the probability of picking a red counter on:
The 1st pick
The 2nd pick

22. The Multiplication Rule
For events which use the word AND we use the multiplication rule
P(A  B) = P(A) x P(B)

24. Question:
When 2 dice are thrown what is the probability of getting
4 or more on each die
2 sixes

25. Question
A gambler must throw a 6 with a single die to win a prize.
Find the probability that he wins on the 3rd attempt

26. Find the probability that:
Question
A bag contains 5 red discs and 3 blue discs. A disc is selected at random and is not replaced.
Find the probability that:
The 1st 2 discs are Red?
The 1st 2 discs are blue?
The first 2 discs are not blue?

27. NOTE: If a question says ‘at least one’ then we must use the following
‘At Least one’ Questions
NOTE: If a question says ‘at least one’ then we must use the following
1 – (Probability of the event not happening)

28. If we you are asked to investigate whether 2 events are independent.
We use the formula
P(A  B) = P(A) x P(B)
and do the following:
Find the left hand side: P(A  B)
Find the right hand side: P(A) x P(B)
If they are independent the left hand side will equal the right hand side

29. We can also prove 2 events are independent if we can prove that
P(A|B) = P(A)
P(B|A) = P(B)