QUESTIONS:
2014; 1a,b
2014; 3c
2013; 1a
theoretical probability
Probability (event)=
number of favourable outcomes
number of possible outcomes
With theortical probability, any
given probability outcome of an activity
is considered to have an equaly likely
chance of occuring as any other probability outcome
for instance
The probability of an event occuring is CALCULATED
based on theoretical data.
EVENT: set of outcomes of intrest.
SAMPLE SPACE: set of all possible outcomes of an
activity.
You will either be given data from which you can calculate the probability of an event occuring within an activity (e.g. apples), or you will not be given data therefore
you assume that the probability is the same for every
given outcome (e.g. dice).
A buisness has 360 staff where 240 work in the
factory and the remainder in the office. Of those
who work in the factory, 60% are male. 75% of office
workers are female.
An employee is selected at random, what is the
probability that they are:
-A male office worker
-A female factory worker
For example, if in a study of 580 apples you
were told 219 were organically grown while 361
were non-organically grown, the probability of
an apple being organically grown would be:
Prob (organically grown)= 219
580
For example, when a fair 6 sided dice is rolled it
is assumed that there is an equally likely chance
that it will land on any side. Therefore the probability of it landing on any given side is: Prob
(landing on 1, 2, 3, 4, 5 or 6)= 1
6
practice Question
A buisness has 360 staff where 240 work in the factory and the remainder in the office.
Of those who work in the factory, 60% are male. 75% of office workers are female.
Solve
An employee is selected at random, what is the probability that they are:
-A male office worker
-A female factory worker
Step One
Step Two
Put the given information in
a table:
Define variables
Construct table
Find the required probabilities
Probability 1
variable 1: place of work
variable 2: gender
male
female
factory
office
male
factory
office
female
Fill in other
values
TOTAL
240
144
TOTAL
male (factory) = 60% of 240
= 0.6 . 240
= 144
360
male
female
TOTAL
factory
office
144
96
240
30
90
120
TOTAL
174
186
360
(6)= 174-144
male and office worker
total number of employees
Find using data in table:
TOTAL
TOTAL
Fill in known
values
P(male office worker) =
(5)= 360-186
(3)= 240-144
male
female
TOTAL
factory
office
144
96
240
30
90
120
TOTAL
174
186
360
P(male office worker) = 30
360
Probability 2
P(female factory worker) =
= 1
12
male and office worker
total number of employees
male
female
TOTAL
factory
office
144
96
240
30
90
120
TOTAL
174
186
360
P(male office worker) = 96
360
studytime.co.nz
facebook.com/studytimenewzealand
total number of
employees= 360
Find using data in table:
(1)= 360-240
(2) female (office) = 75% of 120
= 0.75 . 120
= 90
(4)= 96+90
male and office
worker= 30
And get
female and factory
worker= 96
total number of
employees= 360
= 4
15
P(male office worker) =
1
12
P(male office worker) = 4
15