Probability Worksheet — GCSE — Intermediate

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

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

35 views

0 downloads

Exploring Probability: Intermediate Challenges

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

Name:

Date:

Score:

Instructions: This worksheet is designed to deepen your understanding of probability concepts. You will solve problems, interpret data, and apply probability rules to various scenarios. Ensure you show all your working clearly.

Basic Probability Calculations

Calculate the probability of each event occurring. Express your answers as fractions in their simplest form.

1. A bag contains 3 red balls, 5 blue balls, and 2 green balls. What is the probability of drawing a red ball?

2. A die is rolled once. What is the probability of rolling an even number?

3. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a heart?

Compound Probability

Calculate the probability of the following compound events. Assume all events are independent.

1. Flipping a coin twice, what is the probability of getting two heads?

2. Rolling two dice, what is the probability of getting a sum of 7?

3. Drawing two cards from a deck without replacement, what is the probability of both being aces?

Probability Trees

Use the probability tree diagram to calculate the probabilities of the following outcomes.

Event	Outcome 1	Outcome 2	Outcome 3
First Flip	Heads	Tails
Second Flip	Heads	Heads	Tails

1. What is the probability of getting heads followed by tails?

2. What is the probability of getting two heads?

Expected Value

Calculate the expected value for each scenario. Show your calculations clearly.

1. A game involves rolling a fair six-sided die. You win £10 if you roll a 6, and lose £2 if you roll any other number. What is the expected value of playing the game once?

2. A raffle ticket costs £5, and the prize is £100. If there are 50 tickets sold, what is the expected value of buying one ticket?

Probability in Real-Life Contexts

Read the scenario and calculate the probability of the given events. Provide your answers as fractions.

A survey shows that 60% of people prefer tea over coffee. If you randomly select 5 people, what is the probability that:

1. Exactly 3 prefer tea?

2. At least 4 prefer tea?

Conditional Probability

Calculate the conditional probability for each scenario. Use the formula P(A|B) = P(A and B) / P(B).

1. In a class of 30 students, 18 are girls and 12 are boys. If 5 girls and 3 boys play football, what is the probability that a randomly selected football player is a girl?

2. A box contains 4 red, 3 blue, and 2 green marbles. If a marble is drawn and it is not green, what is the probability that it is red?