UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Education
⋄
ASSESSMENT 03
Year Module — 2026
⋄
Module Code: MIP2602
Module Name: Mathematics for Intermediate Phase Teach-
ers IV
Assignment No.: Assessment 03
Due Date: 26 June 2026
Year: 2026
Submitted in partial fulfilment of the requirements for
Mathematics for Intermediate Phase Teachers IV (MIP2602)
at the University of South Africa.
,UNISA | MIP2602 Assessment 03 — 2026
Section A: Foundations of Probability
Probability is a foundational concept in the Intermediate Phase mathematics curriculum,
providing learners with the tools to reason about likelihood and uncertainty. Research indi-
cates that learners at this stage frequently develop misconceptions about probability because
they conflate relative frequency with absolute counts (Batanero and Álvarez-Arroyo, 2024). A
sound conceptual foundation is therefore essential before learners engage with more complex
probability ideas.
Question 1: Basic Understanding
1.1 Theoretical Probability of Each Colour
A bag contains 3 red, 4 blue, 2 green, and 1 yellow marble, giving a total of 3 + 4 + 2 + 1 = 10
marbles.
Theoretical probability is defined as:
number of favourable outcomes
P (event) =
total number of possible outcomes
The theoretical probability for each colour is calculated as follows:
Table 1: Theoretical Probability of Each Marble Colour
Colour Number of Mar- Total Marbles Probability
bles
3
Red 3 10 P (Red) = = 0.3
10
4
Blue 4 10 P (Blue) = = 0.4
10
2
Green 2 10 P (Green) = =
10
0.2
1
Yellow 1 10 P (Yellow) = =
10
0.1
1.1.1 Probability of Selecting an Orange Marble
There are no orange marbles in the bag. Since there are zero orange marbles among the 10
marbles, the probability of selecting an orange marble is:
Page 1 of 21
, UNISA | MIP2602 Assessment 03 — 2026
0
P (Orange) = =0
10
This is an impossible event. A probability of 0 means the event cannot occur under any cir-
cumstances because the outcome does not exist in the sample space (UNISA, 2026). This
is a useful teaching moment: it demonstrates to learners that probability values range from
0 (impossible) to 1 (certain), and that an outcome with no favourable cases always yields a
probability of zero.
1.2 Ranking Colours from Most Likely to Least Likely
Without calculating, the colours can be ranked by simply comparing the number of marbles
of each colour. More marbles of a particular colour means more favourable outcomes, which
directly increases the likelihood of selection.
1. Blue (4 marbles) — most likely, as it has the greatest number of marbles in the bag.
2. Red (3 marbles) — second most likely.
3. Green (2 marbles) — third most likely.
4. Yellow (1 marble) — least likely, as only one marble out of ten is yellow.
The justification is proportional reasoning: the more marbles a colour has relative to the total,
the greater its share of the sample space. Blue occupies four of the ten positions, making it
the most probable outcome (Batanero and Álvarez-Arroyo, 2024).
1.3 Correcting the Learner’s Misconception
Why the statement is incorrect:
The learner stated that “the probability of selecting a blue marble is 4.” This statement is in-
correct because probability values are always expressed as a number between 0 and 1 inclusive
(or as a percentage between 0% and 100%). The value 4 lies outside this range and therefore
cannot represent a probability. The learner has confused the count of blue marbles (4) with
the probability of selecting a blue marble (Batanero and Álvarez-Arroyo, 2024).
How to help the learner:
A teacher should use the marble activity itself to build conceptual understanding. The follow-
Page 2 of 21
College of Education
⋄
ASSESSMENT 03
Year Module — 2026
⋄
Module Code: MIP2602
Module Name: Mathematics for Intermediate Phase Teach-
ers IV
Assignment No.: Assessment 03
Due Date: 26 June 2026
Year: 2026
Submitted in partial fulfilment of the requirements for
Mathematics for Intermediate Phase Teachers IV (MIP2602)
at the University of South Africa.
,UNISA | MIP2602 Assessment 03 — 2026
Section A: Foundations of Probability
Probability is a foundational concept in the Intermediate Phase mathematics curriculum,
providing learners with the tools to reason about likelihood and uncertainty. Research indi-
cates that learners at this stage frequently develop misconceptions about probability because
they conflate relative frequency with absolute counts (Batanero and Álvarez-Arroyo, 2024). A
sound conceptual foundation is therefore essential before learners engage with more complex
probability ideas.
Question 1: Basic Understanding
1.1 Theoretical Probability of Each Colour
A bag contains 3 red, 4 blue, 2 green, and 1 yellow marble, giving a total of 3 + 4 + 2 + 1 = 10
marbles.
Theoretical probability is defined as:
number of favourable outcomes
P (event) =
total number of possible outcomes
The theoretical probability for each colour is calculated as follows:
Table 1: Theoretical Probability of Each Marble Colour
Colour Number of Mar- Total Marbles Probability
bles
3
Red 3 10 P (Red) = = 0.3
10
4
Blue 4 10 P (Blue) = = 0.4
10
2
Green 2 10 P (Green) = =
10
0.2
1
Yellow 1 10 P (Yellow) = =
10
0.1
1.1.1 Probability of Selecting an Orange Marble
There are no orange marbles in the bag. Since there are zero orange marbles among the 10
marbles, the probability of selecting an orange marble is:
Page 1 of 21
, UNISA | MIP2602 Assessment 03 — 2026
0
P (Orange) = =0
10
This is an impossible event. A probability of 0 means the event cannot occur under any cir-
cumstances because the outcome does not exist in the sample space (UNISA, 2026). This
is a useful teaching moment: it demonstrates to learners that probability values range from
0 (impossible) to 1 (certain), and that an outcome with no favourable cases always yields a
probability of zero.
1.2 Ranking Colours from Most Likely to Least Likely
Without calculating, the colours can be ranked by simply comparing the number of marbles
of each colour. More marbles of a particular colour means more favourable outcomes, which
directly increases the likelihood of selection.
1. Blue (4 marbles) — most likely, as it has the greatest number of marbles in the bag.
2. Red (3 marbles) — second most likely.
3. Green (2 marbles) — third most likely.
4. Yellow (1 marble) — least likely, as only one marble out of ten is yellow.
The justification is proportional reasoning: the more marbles a colour has relative to the total,
the greater its share of the sample space. Blue occupies four of the ten positions, making it
the most probable outcome (Batanero and Álvarez-Arroyo, 2024).
1.3 Correcting the Learner’s Misconception
Why the statement is incorrect:
The learner stated that “the probability of selecting a blue marble is 4.” This statement is in-
correct because probability values are always expressed as a number between 0 and 1 inclusive
(or as a percentage between 0% and 100%). The value 4 lies outside this range and therefore
cannot represent a probability. The learner has confused the count of blue marbles (4) with
the probability of selecting a blue marble (Batanero and Álvarez-Arroyo, 2024).
How to help the learner:
A teacher should use the marble activity itself to build conceptual understanding. The follow-
Page 2 of 21
