Without Replacement: Fluency & Practice
Mathematics
GCSE Higher
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focused on calculating probabilities in scenarios involving without replacement, designed for GCSE Higher students to develop procedural fluency and reasoning skills.
Worksheet Preview
Full preview • 11 questions
Without Replacement: Fluency & Practice
Subject: MathematicsGrade: GCSE Higher
Name:
Date:
TeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizz
Untitled Worksheet
Grade GCSE Higher
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
A bag contains 5 red, 3 blue, and 2 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?
[2 marks]2.
Construct a tree diagram to show all possible outcomes when drawing two cards without replacement from a deck containing 4 aces and 8 other cards. Label each branch with the corresponding probability.
[4 marks]3.
Calculate the probability of drawing two different colors in succession from a bag containing 6 yellow and 4 purple balls, without replacement.
[3 marks]4.
A box has 7 black and 3 white balls. Two balls are drawn without replacement. What is the probability that at least one white ball is drawn?
[3 marks]5.
A student draws two marbles without replacement from a bag containing 5 red, 4 blue, and 1 yellow marble. What's the probability that the student draws a red marble first and a blue marble second?
[3 marks]6.
Explain why the probability of drawing a king then a queen without replacement from a standard deck differs from drawing a queen then a king. Use a tree diagram to support your explanation.
[4 marks]7.
A random sample of 10 students is selected without replacement from a class of 30. If 6 students are wearing glasses, what is the probability that exactly 2 students with glasses are in the sample?
[4 marks]8.
Construct a tree diagram to represent drawing two different colored balls from a container with 3 red and 3 blue balls, without replacement. Label each branch with probability.
[4 marks]9.
A bag has 4 green and 6 yellow balls. Two balls are drawn at random without replacement. Find the probability that both balls are yellow.
[3 marks]10.
Identify and correct the mistake in the following reasoning: 'The probability of drawing a red then a blue ball without replacement is the same as drawing a blue then a red ball.'
[3 marks]11.
A box contains 5 white and 5 black balls. Two balls are drawn without replacement. What is the probability that both are white?
[2 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet