Assessment: Probability and Sample Space

Subject: Mathematics | Year: 7

Name: _________________________ Class/Set: ____________ Date: ____________

Section A: Knowledge Check (Multiple Choice)

Mark the correct answer.

Q1: A fair six-sided die is rolled once. What is the theoretical probability of rolling an even number? a) ☐ 1/6 b) ☐ 3/6 c) ☐ 4/6 d) ☐ 1/2

Q2: The probability that it will rain tomorrow is 0.35. What is the probability that it will NOT rain tomorrow? a) ☐ 0.35 b) ☐ 1.35 c) ☐ 0.65 d) ☐ 0.75

⇨ The table below shows the distribution of different coloured counters found in a single velvet bag used for a probability experiment.

Counter Colour	Quantity
Red	5
Blue	3
Green	2
Yellow	10

Q3: Using the table above, what is the probability of picking a blue counter at random? a) ☐ 3/10 b) ☐ 3/17 c) ☐ 3/20 d) ☐ 1/3

Q4: Which of the following best describes a 'Sample Space'? a) ☐ The number of times an event actually happens. b) ☐ A list or diagram showing all possible outcomes of an event. c) ☐ The probability of an event happening twice. d) ☐ A measurement of how likely an event is to occur.

Q5: A spinner has five equal sections numbered 1 to 5. If the spinner is spun 200 times, how many times would you expect it to land on the number 4? a) ☐ 20 times b) ☐ 40 times c) ☐ 50 times d) ☐ 80 times

Section B: Application (Written Answers)

Answer in the spaces provided.

Q6: A bag contains 12 cards, numbered 1 to 12. A card is drawn at random. Calculate the probability that the number on the card is a prime number. Give your answer as a fraction in its simplest form. [3 marks]

---

---

---

---

---

---

---

---

⇨ The diagram below represents the sample space for an experiment where a fair 10p coin is tossed and a four-sided spinner (numbered 1, 2, 3, 4) is spun at the same time.

	1	2	3	4
Heads (H)	(H, 1)	(H, 2)	(H, 3)	(H, 4)
Tails (T)	(T, 1)	(T, 2)	(T, 3)	(T, 4)

Q7: Use the sample space diagram to calculate the probability of getting a 'Tail' and an even number. Explain why the result of 100 actual trials might be different from your calculated theoretical probability. [5 marks]

---

---

---

---

---

---

---

---

Total Marks: _______ / 13

---

⚠ TEACHER’S GUIDANCE

💡 Pedagogical Pulse

• Targeting Misconceptions: In Section A, Q2 tests the understanding of complementary events. Ensure students recognise that probabilities sum to 1. In Q3, a common error is using the highest frequency as the denominator rather than the total sum (20).
• Year 7 Scaffolding: For the sample space in Section B, ensure students understand that (H, 1) is a single outcome out of a total of 8.
• Oracy Link: When reviewing Q7, encourage students to use the terms 'expected frequency' vs 'observed frequency' to explain why experimental results fluctuate.

Section A Answers

Q1: b (or d)

Explanation: Even numbers are 2, 4, and 6 (three outcomes). 3/6 simplifies to 1/2. Both b and d are technically correct, though b shows the unsimplified working.

Q2: c

Explanation: 1 - 0.35 = 0.65. Probabilities of exhaustive events must sum to 1.

Q3: c

Explanation: Total counters = 5 + 3 + 2 + 10 = 20. Blue counters = 3. Probability = 3/20.

Q4: b

Explanation: Definition of sample space. Option a refers to frequency, d refers to probability itself.

Q5: b

Explanation: P(4) = 1/5. Expected frequency = 1/5 × 200 = 40.

Section B Guidance

Q6 Guidance

• 1 Mark: Identifying prime numbers between 1 and 12 correctly (2, 3, 5, 7, 11). Note: 1 is not prime.
• 1 Mark: Writing the probability as 5/12.
• 1 Mark: Simplest form check (5/12 is already in simplest form).
• Model Answer: "The prime numbers between 1 and 12 are 2, 3, 5, 7, and 11. There are 5 prime numbers. Since there are 12 cards in total, the probability is 5/12."

Q7 Guidance

• 1 Mark: Identifying relevant outcomes from the table (T, 2) and (T, 4).
• 1 Mark: Stating the probability as 2/8 or 1/4.
• 1 Mark: Identifying that theoretical probability is based on ideal conditions.
• 1 Mark: Identifying that experimental probability (relative frequency) involves chance/randomness.
• 1 Mark: Mentioning that a larger number of trials would make the experimental result closer to the theoretical one.
• Model Answer: "From the sample space, there are 8 possible outcomes. The outcomes with a Tail and an even number are (T, 2) and (T, 4), so the probability is 2/8 or 1/4. In 100 actual trials, the result might be different because theoretical probability only predicts what should happen in the long term. Random chance means that in a small sample of 100, the results will vary."