Probability Worksheet — GCSE — Beginner

Probability worksheet for Key Stage 4 / GCSE (Ages 14-16). Beginner level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 4 / GCSE (Ages 14-16)•Probabilitybeginner

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Understanding Probability: A Beginner's Guide

Key Stage 4 / GCSE (Ages 14-16) - Beginner Level

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Instructions: This worksheet introduces you to the basics of probability. You'll explore concepts through a variety of activities, including problem-solving, data analysis, and scenario-based questions. Follow the instructions carefully to complete each task.

Introduction to Probability

Read the following statements and determine whether they are certain, likely, unlikely, or impossible. Write your answer in the box provided.

1. It will snow in July in the UK.

2. A coin tossed will land on heads.

3. The sun will rise tomorrow.

4. You will win the lottery this week.

Calculating Simple Probability

Calculate the probability of each event occurring. Express your answer as a fraction in its simplest form.

1. Rolling a 3 on a standard six-sided die.

2. Drawing a heart from a standard deck of 52 cards.

3. Picking a red marble from a bag containing 3 red, 4 blue, and 5 green marbles.

4. Flipping a coin and getting tails.

Probability with a Spinner

A spinner is divided into 8 equal sections: 3 red, 2 blue, 2 green, and 1 yellow. Calculate the probability of the spinner landing on each colour.

1. Red

2. Blue

3. Green

4. Yellow

Probability in Real-Life Scenarios

Consider each scenario and calculate the probability of the given event. Express your answers as fractions.

1. There are 10 students in a class. If 4 students are chosen at random, what is the probability that all are girls, given there are 6 girls and 4 boys?

2. A bag contains 5 apples and 3 oranges. What is the probability of picking an apple?

Data Analysis with Probability

Analyse the data in the table and answer the questions below.

Event	Number of Occurrences	Probability
Heads	30
Tails	20
Even Number on Die	25
Odd Number on Die	15

1. Calculate the probability of each event occurring.

2. Which event is most likely to occur?

Exploring Theoretical vs Experimental Probability

Compare theoretical and experimental probabilities using the data provided. Answer the questions that follow.

A coin was flipped 100 times, resulting in 55 heads and 45 tails.

1. What is the theoretical probability of flipping heads?

2. What is the experimental probability of flipping heads based on the data?

3. Explain any differences between the theoretical and experimental probabilities.

Probability with Multiple Events

Calculate the probability of the following combined events. Express your answers as fractions.

1. Rolling a 4 on a die and flipping a head on a coin.

2. Drawing a red card and then a black card from a deck of cards without replacement.

Extended Writing: Probability in Decision Making

Write an essay discussing how probability can influence decision-making in real-life situations. Use examples to illustrate your points. Consider both risks and benefits.

Evaluate the role of probability in decision-making processes. Discuss how understanding probability can aid in making informed decisions in areas such as finance, healthcare, and everyday life. [15 marks]

Answer Key

Activity 1: Impossible ; Likely ; Certain ; Impossible

Activity 2: 1/6 ; 1/4 ; 3/12 or 1/4 ; 1/2

Activity 3: 3/8 ; 2/8 or 1/4 ; 2/8 or 1/4 ; 1/8

Activity 4: 1/210 ; 5/8

Activity 5: 30/90 or 1/3 ; 20/90 or 2/9 ; 25/90 or 5/18 ; 15/90 or 1/6 ; Heads

Activity 6: 1/2 ; 55/100 or 11/20 ; Theoretical probability assumes equal likelihood, while experimental results can vary due to chance.

Activity 7: 1/12 ; 26/51

Activity 8: [Essay response will vary]