Post on 03-Jan-2016
Probability (1)Probability (1)
Outcomes and EventsOutcomes and Events
Let C mean “the Event a Court Card (Jack, Queen, King) is chosen”
Let D mean “the Event a Diamond is chosen”
Probability Notation
n(C) means “the number of outcomes favourable to C”
n(D) means “the number of outcomes favourable to D”
n(C) = 12 (4x3=12 Court cards in a pack of 52)
n(D) = 13 (13 Diamonds in a pack of 52)
Venn Diagram
CThe court
cards
DDiamonds
Outside is all other cards
Cards that are Court Cards and Diamond
C D
Probability Notation (2)
n(C) = 12 (12 Court cards in a pack of 52)
n(D) = 13 (13 Diamonds in a pack of 52)
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 is both a court card and diamond is chosen”
n(C D) = 3 (the Jack, Queen, King Diamonds)
n(C n D) means “the number of outcomes of both events C and D”
Fish ‘n’ Chips
Fish Chips
Venn Diagram
F CF n C
Venn Diagram
CThe court
cards
DDiamonds
Outside is all other cards
C D
3
12 13
30 ?
?
?
?
Venn Diagram
C D
C DEntire Shaded area is the ‘Union’
Venn Diagram
C D
C Dn(C)=12
n(C D) = 3
n(D)=13
n(C D) = n(C) + n(D) - n(C D)
12n(C D) =
Avoid double-counting these
+ 13 - 3 = 22
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(C D) = n(C) + n(D) - n(C D)
Venn Diagram
C
n(C) = 12
n(C’) = 40
C’The complement
?
Cn(C) = 12
P(C) The probability
of C
= n(C) = 12 = 3 52 52 13
C’
P(C’)
n(C’) = 40
= n(C’) = 40 = 10 52 52 13
P(C’) = 1 - P(C)
Venn Diagram
C DC DP(C) = n(C)/52 P(D) =
n(D)/52P(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”
___52
___52
______52
______52
Venn Diagram
C DC DP(C) = n(C)/52
n(C D) = n(C) + n(D) - n(C D)
P(D) = n(D)/52
P(CnD) = n(CnD)/52
P(C D) = P(C) + P(D) - P(C D)
Venn Diagram
C D
If there is no overlap, it means there are no outcomes in common
n(C D) = 0
These are known as MUTUALLY EXCLUSIVE EVENTS
For example:- C means “picking a Court Card” D means “picking a Seven”
Probability Notation (4)
P(C) The probability
of C
= n(C) 52
P(C’) = 1 - P(C)
P(C D) = P(C) + P(D) - P(C D)
P(C D) = P(C) + P(D)
For mutually exclusive events
n(C D) = n(C) + n(D)
Consider a series of 60 Maths Lessons
If ...
P(L G) = ?
P(L) = ?
P(G) = ?
P(L G) = ?
Lisa is absent 40 times
Gus is absent 18 times
In 5 lessons they were both absent
What does mean (in words) ?P(L G)
5/60 = 1/12
18/60 = 3/10
40/60 = 2/3
L G
L GP(L G) = 1/12
P(L)=2/3 P(G)=3/10
P(L G) = P(L) - P(L G)+ P(G)
2/3P(L G) = + 3/10 - 1/12 = 53/60“In 53/60 lessons Lisa or Gus was absent”
they are both absent
Consider a series of 60 Maths LessonsIf ...
P(L) = 2/3
P(G) = 3/10
Lisa absent the most
P(L G) = 1/12
P(L G) = 53/60
Gus absent the most
Both absent
Either is absent
P(L’) = ?
What is the probability Lisa isn’t absent?
P(L’) = 1 - P(L) = 1 - 2 = 1 3 3