Probability (1) Outcomes and Events

1
Probability (1)Outcomes and Events
2
Probability Notation
Let C mean the Event a Court Card (Jack, Queen,
King) is chosen
Let D mean the Event a Diamond is chosen
n(C) means the number of outcomes favourable to
C
n(C) 12 (4x312 Court cards in a pack of 52)
n(D) means the number of outcomes favourable to
D
n(D) 13 (13 Diamonds in a pack of 52)
3
Venn Diagram
Cards that are Court Cards and Diamond
Outside is all other cards
4
Probability Notation (2)
Let C mean the Event a Court Card is chosen
Let D mean the Event a Diamond is chosen
n(C) 12 (12 Court cards in a pack of 52)
n(D) 13 (13 Diamonds in a pack of 52)
n(C n D) means the number of outcomes of both
events C and D
5
Venn Diagram
F n C
C
F
6
Venn Diagram
13
12
3
30
Outside is all other cards
7
Venn Diagram
C
8
Venn Diagram
n(D)10
n(C)9
D
C
n(D)
n(C)
22
13
- 3
12
9
Probability Notation (3)
Let C mean the Event a Court Card is chosen
Let D mean the Event a Diamond is chosen
C D means the Event a card that chosen is a
court card or a diamond
n(C u D) means the number of outcomes of C or D
n(D)
n(C)
10
Venn Diagram
C
n(C) 12
n(C) 40
?
11
C
P(C) 1 - P(C)
C
n(C) 40
n(C) 12
P(C)
12
Venn Diagram
C
D
P(C) n(C)/52
P(D) n(D)/52
P(CnD) n(CnD)/52
P(CnD) n(CnD)/52 3/52
The probability of choosing a card that is both
a Court Card and a Diamond is 3/52
13
Venn Diagram
C
D
P(C) n(C)/52
P(D) n(D)/52
P(CnD) n(CnD)/52
n(D)
n(C)
______ 52
______ 52
___ 52
___ 52
14
Venn Diagram
C
D
If there is no overlap, it means there are no
outcomes in common
These are known as MUTUALLY EXCLUSIVE EVENTS
For example- C means picking a Court Card
D means picking a Seven
15
Probability Notation (4)
n(C) 52
P(C) 1 - P(C)
16
Consider a series of 60 Maths Lessons
If ...
Lisa is absent 40 times
40/60 2/3
P(L) ?
Gus is absent 18 times
P(G) ?
18/60 3/10
In 5 lessons they were both absent
5/60 1/12
What does mean (in words) ?
17
P(G)3/10
P(L)2/3
G
L
they are both absent
P(G)
P(L)
53/60
3/10
- 1/12
2/3
In 53/60 lessons Lisa or Gus was absent
18
Consider a series of 60 Maths Lessons
If ...
Lisa absent the most
P(L) 2/3
Gus absent the most
P(G) 3/10
Both absent
Either is absent
P(L) ?
What is the probability Lisa isnt absent?
P(L) 1 - P(L)