Quiz: Probability and Events

Subject: Mathematics | Year: 8

Questions (Student Sheet)

Name: _________________________ Class/Set: ____________ Date: ____________

Q1: Two events are described as being 'mutually exclusive'. What does this term specifically mean in probability? a) ☐ The events must have the same probability of occurring. b) ☐ The two events cannot happen at the same time. c) ☐ The outcome of the first event changes the probability of the second. d) ☐ The sum of the probabilities of the two events must be exactly 0.5.

Q2: If the probability of an event occurring is represented by p, which calculation correctly determines the probability of the event NOT occurring? a) ☐ 1 + p b) ☐ p - 1 c) ☐ 1 - p d) ☐ 1 ÷ p

Q3: The probability that a train arrives on time is 0.72. What is the probability that the train is late? a) ☐ 0.38 b) ☐ 0.22 c) ☐ 1.72 d) ☐ 0.28

⇨ The data provided in the table below shows the probabilities of a biased four-sided spinner landing on specific numbers.

Number	1	2	3	4
Probability	0.2	0.35	0.15	x

Q4: Based on the table above, what is the value of x? a) ☐ 0.3 b) ☐ 0.7 c) ☐ 0.4 d) ☐ 0.25

Q5: A bag contains only red, blue, and green counters. The probability of picking a red counter is 1/5 and the probability of picking a blue counter is 2/5. What is the probability of picking a green counter? a) ☐ 3/5 b) ☐ 2/5 c) ☐ 1/5 d) ☐ 4/5

Score: _______ / 5

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⚠ TEACHER’S GUIDANCE

💡 Pedagogical Insights:

• Explain: Emphasise that for a set of mutually exclusive outcomes that cover all possibilities (exhaustive events), the sum must be exactly 1.
• Model: Use the "complementary event" rule (P(not A) = 1 - P(A)) to help students solve problems where only one outcome is missing.
• Address Misconception: Watch for students who think probabilities sum to 100 rather than 1. Remind them that 1 represents 100% certainty.

Answer Key & Explanations

Q1: b

Explanation: Mutually exclusive events are those that cannot occur simultaneously (e.g., a coin cannot land on both Heads and Tails at the same time). Option A describes 'equally likely' events, and Option C describes 'dependent' events.

Q2: c

Explanation: The sum of the probability of an event happening and it not happening is always 1. Therefore, to find the probability of it not happening, we subtract the known probability from 1.

Q3: d

Explanation: Using the subtraction rule: 1.00 - 0.72 = 0.28. A common error (Option A) occurs when students miscalculate the subtraction across the decimal point.

Q4: a

Explanation: The sum of all probabilities in the table must be 1. Adding the known values: 0.2 + 0.35 + 0.15 = 0.7. To find x: 1 - 0.7 = 0.3.

Q5: b

Explanation: First, add the probabilities of the red and blue counters: 1/5 + 2/5 = 3/5. Since these are the only colours in the bag, the remaining probability must be green: 5/5 - 3/5 = 2/5.