Scottish Survey of Literacy and Numeracy
Support Materials
Ideas of chance and uncertainty: Second Level
Part 2
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Second Level: Ideas of Chance and Uncertainty
Experience and Outcome:
MNU 2-22
I can conduct simple experiments involving chance and communicate my predictions and
findings using the vocabulary of probability.
Learning Intention
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
Success Criteria
I will explore how the probability of an
event lies between 0 and 1 i.e.
impossible and certain.
I am able to understand, for example:
equal chance; 50 / 50; one out of two
chances; percentage chance.
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

I can use a scale of 0 – 1 to describe
where an event lies and identify the half
way point as an even chance, or a
50/50 chance.
I can describe an impossible chance as
0%, a certain chance as 100% and an
evens chance as 50%.
I can use number to describe a
probability e.g. a one in three chance.
Key Vocabulary:
Certain , impossible, likely, likelihood, unlikely, very unlikely, how likely, very likely, highly
unlikely, highly likely, chance, good chance, poor chance, evens, probability, scale, even chance,
fair, unfair, fifty –fifty, equal chance, percentage chance, one in two, two in three etc
Learning and Teaching Ideas
It is important that pupils understand the various ways in which probability can be presented in
order to communicate predictions and findings when conducting experiments.
*Reflective questions:
What kind of concrete material do you think would enhance learning and teaching of this aspect?
What other sources could be accessed to aid the understanding of ‘Ideas of Chance and
Uncertainty’?
Probability Scale
On the probability scale from impossible to certain, using words (see above) discuss how these
words could be written as a percentage (or as a decimal fraction or fraction) and ask pupils to
suggest statements using these percentages e.g. there is 50% chance that if you toss a coin it
will land on a head.
0%
0
Impossible
50%
0.5
½
even chance
Fifty-fifty
100%
1
certain
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*Reflective questions:
How well are the connections between percentages, decimal fractions and fractions understood
by your pupils?
How can I help my pupils develop their understanding of these connections?
True, False or unsure statements
On hearing the following statements pupils hold up a ‘true’, ‘false’ or ‘unsure’ card and explain
their choice:
A certain chance of something happening is the same as a 100% chance of it happening.
In a game of noughts and crosses you have a 50% chance of winning.
Probability lies between 0 and 1.
If you buy double the number of lottery tickets then you are more likely to win.
A 50% chance is the same as an even chance.
You have a 50% chance of rolling a die and landing on an odd number.
The probability of landing on an 8 when rolling a die is 0.
You have a 1 in 4 chance of selecting a club from a pack of cards.
In a class of 20 pupils, the probability of two pupils being born on the same day is 1.
The probability of getting exactly three heads in six coin tosses is 0.5.
*Reflective questions:
Is there another way of writing a 1 in 4 chance?
How do you encourage pupils to describe probability in a variety of ways?
The Monty Hall Problem
In a quiz show the contestant is faced with three doors. Behind one door is a new Ferrari and
behind the other two are turnips. The contestant chooses a door and wins whichever prize is
behind that door.
The host of the show knows where the Ferrari is hiding and when the contestant chooses a door
he then opens one of the two remaining doors to reveal a turnip. The contestant must then
decide whether to stick with his original choice, or to switch to the other door.
How should the contestant answer in order to maximise his chances of winning a Ferrari, and
what is the reason for this decision?
Solution
They should change their original choice of door to the other door which has not been opened.
Originally their chosen door had only a 1 in 3 chance of winning and a 2 in 3 chance of losing, i.e.
they are more likely to have chosen a losing door initially, so should change their choice of door
to increase their chances of winning.
http://www.bbc.co.uk/learningzone/clips/the-monty-hall-problem-probabilities-and-game-showsexplained/11261.html (Monty Hall problem explained)
This problem is good for discussing the vocabulary, e.g. a 1 in 3 chance and also when faced
with the remaining two doors pupils assume incorrectly that they then have a 50/50 chance of
winning. It is good to explore why this is not the case.
*Reflective questions:
Can pupils identify other quiz shows in which probability can be used to predict your chance of
winning?
How do you explore the use of probability in our everyday lives?
When faced with making choices, how can our understanding of probability help?
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Cross curricular contexts for Learning
*Reflective questions:
How does ‘ideas of chance and uncertainty’ contribute to the development of skills for learning,
life and work?
Reflecting on your curriculum plan, where do you see possible links with other curricular areas?
Planning for progression
There are lots of probability clips on the BBC Learning Zone:
http://www.bbc.co.uk/learningzone/clips/
(search for probability – includes birthday likelihoods, tossing a coin etc)
http://www.educationscotland.gov.uk