QUESTIONS:
2013; 1bii
2012; 2b
2012; 3ciii
CONDITIONAL PROBABILITY
(data in table)
P(A B)= P(A and B)
P(B)
The probability of an event
occuring, given that another
event has already occured.
B
B’
TOTAL
A
AB
AB’
A
A’
A’B
A’B’
B
B’
TOTAL
for instance
EVENT: set of outcomes of intrest.
With conditional probabilities, the second event can only
occur because the first event has already occured. The
occurance of the first event changes the likelyhood of
the second event occuring.
Conditional probabilities can be calculated for events
where the data is given in a question or displayed in
tables (two way), venn diagrams or probabilities trees.
A’
A+A’ or B+B’
A New Zealand tour company collected data on 850 of its
passengers and found that 408 were male, 60% were from
overseas and of the overseas passengers, 187 were male.
What is the probability that a passenger, who was a New
Zealander, was female?
When calculating conditional probabilites for
events where the data is displayed in a tables,
the equation does not have to be used. Instead
bthe sample space can be reduced so that the
probability is not out of the total sample, but
just the total of the data in a specific row or
column.
When calculating conditional probabilites for
events where the data is displayed in venn
diagrams, the equation also does not have to
be used.
practice Question
Solve
A New Zealand tour company collected data on 850 of its passengers and found that 408 were
male, 60% were from overseas and of the overseas passengers, 187 were male.
What is the probability that a passenger, who was a New Zealander, was female?
Step One
Step Two
Display data in appropriate
form
Define events
and display
Estimate the size of the sample
group
Event 1: sex of passenger (male or female)
Event 2: where they are from (overseas of New
Zealand)
As there are two catergory variables, and the information into each
varibale has been given as number of passangers, not probabilities , a
two-way table is used.
Construct table
Overseas
Male
NZ
TOTAL
187
408
510
850
Female
TOTAL
Complete table
Overseas
NZ
TOTAL
Male
187
221
408
Female
323
119
442
TOTAL
510
340
850
Conditional
Probability
Although this question does not use the word ‘given’, which hints that the
question is asking for a conditional probability and indicates which event is
given to another, this question is conditional.
P(A B) = P(A and B)
P(B)
P(A) = passenger is female
P(B) = passenger from New Zealand
P(A and B) = passenger a female from New Zealand
60% of 850
0.6 . 850
(3) 408- 187
Overseas
NZ
TOTAL
Male
187
221
408
Female
323
119
442
TOTAL
510
340
850
(2) 850- 408
(5) 510- 187
(4) 340- 221
(1) 850- 510
P(A and B) = 119
P(B) = 340
P(A B) = 119
340
studytime.co.nz
facebook.com/studytimenewzealand
And get
P(A B) = 7/20 or 0.35 (2d.p)
P(A B) = 7/20 or 0.35 (2d.p)