GCSE Maths Practice: probability-scale

Understanding Probability with Coloured Objects

Many GCSE Foundation probability questions use coloured balls, counters, or cubes inside a bag or container. These contexts are ideal for practising simple probability because they clearly show how to compare favourable outcomes to total possible outcomes. In this problem, we are asked to calculate the probability of selecting a red ball from a bag containing both red and blue balls. This allows us to build confidence with fractions, sample spaces, and identifying favourable events.

Total and Favourable Outcomes

The key idea in basic probability is comparing what we want to happen (the favourable outcomes) with everything that could possibly happen (the total outcomes). In this type of scenario:

• The total number of balls represents all possible outcomes.
• The number of balls of the chosen colour represents the favourable outcomes.

Because each ball is equally likely to be selected, probability is simply a matter of dividing the favourable count by the total count.

Step-by-Step Method

1. Identify the total number of balls. Add the red and blue balls together.
2. Count how many balls match the event. Here, the event is selecting a red ball.
3. Write the probability as a fraction. Use the formula favourable ÷ total.
4. Optionally simplify. You may simplify the fraction, but it is not required unless the question specifically asks.

Worked Example 1: Selecting a Blue Ball

If instead you were asked to find the probability of selecting a blue ball, the favourable outcomes would be the number of blue balls. You would then divide that number by the total number of balls. The method stays exactly the same.

Worked Example 2: Mixed Colours with Different Totals

Imagine a bag with 7 green balls and 3 yellow balls. To find the probability of selecting a yellow ball, favourable outcomes = 3 and total outcomes = 10. The probability is written as 3/10. The numbers change, but the process remains consistent.

Worked Example 3: Selecting a Ball of a Different Type

If a bag contained 8 marbles and 12 stones, and you wanted the probability of selecting a stone, you would treat the stones as favourable outcomes and proceed with the same division method.

Common Mistakes to Avoid

• Not counting all items: Some learners miscount the total, forgetting to include all colours or types.
• Reversing the fraction: The favourable outcomes must always be the numerator (top of the fraction).
• Forgetting that each ball is equally likely: The question assumes a fair selection unless stated otherwise.
• Simplifying incorrectly: While simplification can help check accuracy, it is not required unless explicitly asked.

Real-Life Applications

Although coloured balls in a bag are often just an exam example, the thinking behind this type of question is used constantly in real life. Situations such as sampling products in manufacturing, selecting survey participants, analysing medical testing data, and predicting outcomes in games all rely on comparing favourable events with total possibilities. Understanding how to calculate simple probability helps build a foundation for more complex statistical reasoning used in science, business, and daily decision-making.

Frequently Asked Questions

Q1: Does the order matter when selecting just one item?
No. For single-event probability, order is irrelevant. You only care about what is selected, not the order.

Q2: Should I simplify the final fraction?
You may simplify to check your understanding, but both the unsimplified and simplified forms are valid unless the question requires a simplified answer.

Q3: What if the bag contained extra colours?
The method stays the same. Count only the favourable items and divide by the total of all items.

Study Tip

When solving coloured-ball probability questions, quickly write down: total outcomes, favourable outcomes, and then form the fraction. This simple routine ensures accuracy and speed in GCSE exams.