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Probability Starters
NCEA Results
Year 12 and 13 students were surveyed about their NCEA results.
Passed L1
Year 12
Year 13
Still to
achieve
M
25
30
F
22
23
M
25
15
F
55
5
A student is chosen at random. Calculate the following probabilities.
1. The student has passed level 1.
2. A girl has not achieved level 1.
3. The student is a female at year 12.
4. A student who has passed is a girl in year 12.
5. The student is a year 13 boy who is still to achieve.
6. A boy is chosen, what is the probability that he has passed?
Dominos
A full set of dominos contains all the possible pairs
of numbers from 1 to 6 plus blanks.
1. How many dominos are there in a full set?
2. If one domino is selected at random from a full
set, what is the probability it has exactly six dots
on it?
I have a bag and in it are 4 beans, 2 are
yellow and 2 are blue.
If I draw two beans from the bag what is the
probability that they are both blue?
I have a bag and in it are 7 beans, 2 are yellow and 5 are blue.
If I randomly select two beans from the bag what is the probability
of getting one of each colour.
If one of the beans is yellow what is the probability that the other
bean is blue?
Simulation
• A simulation imitates a
real situation.
• It should act as a
predictor of what would
actually happen in
practice.
• It is a model in which
experiments are carried
out so as to estimate
what might happen in
real life.
Simulation using the Calculator
• The random number generator on the
calculator produces 3 digit random
numbers between
0.000 and 0.999
all equally likely.
• For each digit there are 10 possible
outcomes. What are they?
• These digits can be used on their own or
together to simulate outcomes for
probability experiments.
Example
• Using the first two digits only of a random
number we can model or simulate a two
child family.
1
• An odd digit represents a girl. (p= 2 )
• An even digit represents a boy.
• So the random number 0.234 will
represent the family of boy(2) then girl(3),
ignore the 4.
Simulation
• When a child is born it is equally likely to
be a boy or a girl.
• Use the random number function on your
calculator to simulate a three child family.
• Repeat 9 more times. (10 families in total)
• Use your data to estimate the proportion of
three child families which have all children
the same sex.
Using the random number function of the calculator.
Using the 3 digits of a random number. An odd digit will represent a
boy and an even digit will represent a girl. Even and odd occur with
equal probabilities same as boys or girls)
Generate a random number to represent the three members of
the family. Record the results.
Eg. 0.479 will be recorded as GBB (even, odd, odd)
Repeat the trial 10 times.
BGB
GBB
GGB
GGB
BBB
BBG
GBB
GBB
GBG
BBB
Probability of a family being all the same sex is
0.2 (2 from 10)
TRAFFIC LIGHT
SIMULATION
Coming to school each day, Laura rides through 2
traffic lights. The probability that any one light is
green is 0.3, and the probability that it is not green is
0.7
Design and carry out a simulation to estimate the
probability that Laura will find that both lights are
green.
TTRC
• Tool
– Using calc random number function.
– Using the first 2 digits to represent each traffic light.
– If the digit is 1 or 2 or 3 the light is green, otherwise it is red.
• Trial
– Generate one random number to represent one trip to school.
– Record the result.
– Example 0.386 will be green (3) red (8) ignore the 6.
• Results
– Set results out in a table
trip
lights
• Calculations
– From my results we can see that Laura got two greens XX% of the time.