GCSE Maths Practice: probability-scale

Question 1 of 10

Test your skill in calculating simple probabilities from a mixed group of items.

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\( \begin{array}{l}\textbf{A bag holds 5 black balls and 3 white balls.} \\ \textbf{What is the probability of selecting a} \\ \textbf{black ball on one random draw?}\end{array} \)

Choose one option:

List the total outcomes first, then count the favourable ones.

Understanding Probability with Mixed Objects

When working with GCSE Higher probability, a key skill is determining the likelihood of an event when several different types of objects are involved. In this type of question, you are given a situation where items are grouped together, such as coloured balls in a bag. Your task is to calculate the probability of selecting a particular type on a single random draw. This core skill appears frequently in both exams and real-life problem-solving situations.

How Single-Event Probability Works

Probability compares the number of favourable outcomes to the total number of possible outcomes. The formula is:

Probability = favourable outcomes ÷ total outcomes

This creates a fraction between 0 and 1, where values closer to 1 mean an event is more likely. In contexts involving random selection without replacement, but with only one draw, the calculation remains straightforward because picking one item does not trigger changes to the rest of the group.

Step-by-Step Method

  1. Identify the total number of items in the group. This represents all possible outcomes.
  2. Determine how many items match the event you are interested in. These are the favourable outcomes.
  3. Write the probability as a fraction.
  4. Simplify the fraction if possible.

Worked Example 1

A bag holds 4 red cubes and 6 blue cubes. What is the probability of selecting a blue cube?

  • Total cubes: 10
  • Blue cubes: 6
  • Probability = 6/10 = 3/5

Worked Example 2

A box contains 7 metal screws and 1 plastic screw. What is the probability that a randomly chosen screw is metal?

  • Total screws: 8
  • Metal screws: 7
  • Probability = 7/8

Common Mistakes to Watch For

  • Ignoring the total: Some students focus only on the favourable outcomes and forget to count every item.
  • Adding instead of dividing: Probability must be written as a fraction, not a sum.
  • Using percentages incorrectly: You can convert to a percentage, but ensure the fraction is correct first.
  • Overthinking single draws: Replacement only matters when more than one item is drawn.

Real-Life Applications

This skill is not just for exams. People use probability when estimating outcomes in card games, predicting component failure in engineering, analysing scientific samples, or evaluating outcomes in medical studies. Any situation involving a known group and a random event uses this principle.

Frequently Asked Questions

Q1: Do I need to simplify the final fraction?
It is good practice, but if the fraction is already in its simplest form, you can leave it as it is.

Q2: What if the question uses words instead of numbers?
Translate the description into quantities. For example, “more black than white” tells you nothing unless specific totals or ratios are given.

Q3: Is probability always a fraction?
It can be expressed as a fraction, decimal, or percentage, but fractions are most common in GCSE questions.

Study Tip

Whenever you see a probability question involving coloured balls, cards, shapes, or objects, immediately list the total outcomes and favourable outcomes. This quick habit speeds up problem-solving and ensures accuracy.

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