AQA GCSE Mathematics Paper 3 (Foundation), June 2025: Question 14

Calculating Probabilities and Expected Frequency

AQA GCSE Mathematics • Probability Tables • 5 Marks Total

What this question tests

Sum of probabilities: Knowing that the probabilities of mutually exclusive, exhaustive outcomes always sum to 1.
Forming equal shares: Finding an unknown remaining probability and dividing it equally when outcomes are equally likely.
Complementary events: Calculating the probability of an event not happening using P(not A) = 1 − P(A).
Expected frequency: Calculating the expected number of occurrences using Frequency = Total × Probability .

Question 14 (a) [2 marks]

Completing the probability table given P(green) = P(yellow)

Colour	Red	Blue	Green	Yellow
Probability	0.1	0.24	0.33	0.33

📐 Step-by-Step Calculation

Sum known probabilities:
0.1 + 0.24 = 0.34
Find the remaining probability:
1 − 0.34 = 0.66
Share equally between Green and Yellow:
0.66 ÷ 2 = 0.33

✅ Correct Answer & Mark Scheme

0.66 seen or 1 − (0.1 + 0.24) or 0.33 [M1]
Both 0.33 and 0.33 entered correctly into the table (or equivalent fractions/percentages) [A1]

💡 Key Knowledge

The total probability of all possible outcomes for a single event is always 1.
When two outcomes are equally likely, their probabilities are identical: P(green) = P(yellow).
Probabilities can be given as decimals (0.33), fractions (33/100), or percentages (33%). Decimals are the cleanest here.

❌ Common Errors

Decimal alignment slip: Adding 0.1 and 0.24 to get 0.25 (treating 0.1 as 0.01). Always remember 0.1 = 0.10!
Halving error: Forgetting to divide 0.66 by 2, writing 0.66 in both boxes (which gives a total well above 1).

Question 14 (b) [3 marks]

Finding the number of cards that are not blue out of 600

📐 Method 1: Subtraction (Fastest)

Calculate number of blue cards:
600 × 0.24 = 144 blue cards [M1]
Subtract from total cards:
600 − 144 [M1dep]
Final count:
456 [A1]

📐 Method 2: Complementary Probability

Find P(not blue):
1 − 0.24 = 0.76
(or 0.1 + 0.33 + 0.33 = 0.76) [M1]
Multiply probability by total:
600 × 0.76 [M1dep]
Final count:
456 [A1]

🧠 Exam Technique & Follow-Through

Read the bold text: The word not is in bold. A common dropped mark is stopping at 144 (the number of cards that are blue).
Follow-Through Marks (ft): If you made an arithmetic slip in part (a), you can still gain full marks in (b) if you correctly use your incorrect values from the table (e.g. 600 × [0.1 + your green + your yellow]).

❌ Calculation Traps

Leaving the answer as a probability (0.76) rather than calculating the actual number of cards.
Calculating 600 × 0.24 = 144 and giving 144 as the final answer without subtracting from 600.
Non-calculator mental math slip: 600 × 0.24 = 6 × 24 = 144. Always double-check your long multiplication.

Examiner Insight: Method 1 ( 600 − (600 × 0.24) ) is the most robust because it does not rely on your answers to part (a), completely protecting you from carrying forward any previous arithmetic error!