Without Replacement: Error Analysis & Misconceptions
Mathematics
GCSE Higher
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring common errors and misconceptions related to calculating probabilities without replacement, with a focus on understanding and correcting mistakes.
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Without Replacement: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
A bag contains 5 red and 3 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?
[2 marks]2.
Calculate the probability of drawing a blue marble first and then a red marble from the same bag.
[3 marks]3.
A deck has 52 cards. If two cards are drawn without replacement, what is the probability that both are aces?
[2 marks]4.
A box has 10 chocolates: 4 milk, 3 dark, 3 white. Two chocolates are chosen without replacement. What is the probability both are white?
[2 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed reasoning in the grid spaces.
1.
A class has 12 students, 7 boys and 5 girls. Two students are selected at random without replacement. Find the probability that both are girls and explain your reasoning.
[4 marks]2.
A fruit basket contains 8 apples and 6 oranges. Two fruits are picked without replacement. What is the probability that the first is an apple and the second an orange? Explain your steps.
[4 marks]3.
Explain why the probability of drawing two red marbles without replacement is different from drawing two with replacement, and write the correct calculation for the without replacement case.
[4 marks]C
Real-world Applications
Answer all questions with detailed reasoning and calculations.
1.
In a lottery, 50 tickets are numbered from 1 to 50. Three tickets are drawn without replacement. What is the probability that all three are even numbers?
[4 marks]D
Challenge & Extension
Answer these challenging questions. Show your full reasoning and calculations.
1.
A bag contains 4 red, 3 blue, and 2 green balls. If three balls are drawn without replacement, what is the probability that all three are different colors? Explain your reasoning.
[5 marks]2.
A student picks two books from a set of 15, of which 5 are mathematics books. What is the probability that both books are mathematics, and why might a common mistake be made in this calculation?
[5 marks]E
Mixed Review & Error Analysis
Answer all questions. Review the common mistakes in your answers.
1.
A jar has 10 red and 10 black balls. Two balls are drawn without replacement. A student claims the probability both are red is 1/2. Is this correct? Explain and correct if necessary.
[3 marks]2.
Identify the mistake in this reasoning: 'Since there are 5 red and 5 blue balls, the probability of drawing a red then a blue is 1/2.'
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet