Multiplying Along Branches: Mixed Review
Mathematics
Year 9
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet covering Multiplying Along Branches in Tree Diagrams for Year 9 students, including procedural practice, problem-solving, real-world contexts, and extension questions.
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Multiplying Along Branches: Mixed Review
Subject: MathematicsGrade: Year 9
Name:
Date:
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the probability of two independent events both occurring: the first event has a probability of 0.6, and the second event has a probability of 0.5.
[2 marks]2.
A spinner has 4 equal sections numbered 1 to 4. If you spin twice independently, what is the probability of getting a 2 first and a 3 second?
[2 marks]3.
A box contains 3 red balls and 2 blue balls. If a ball is drawn twice with replacement, what is the probability that both balls are red?
[2 marks]4.
In a game, the chance of winning is 0.7. If two independent games are played, what is the probability of winning both?
[2 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed working in the grid spaces provided.
1.
A student chooses a card from a deck, then rolls a die. The probability of drawing a heart is 1/4, and rolling a 5 is 1/6. Assuming independent events, what is the probability the student draws a heart and then rolls a 5?
[3 marks]2.
A factory produces 2% defective items. Two items are selected independently. What is the probability that both are non-defective?
[3 marks]3.
A survey shows 60% of students like chocolate and 50% like vanilla. Assuming independence, what is the probability that a student likes both?
[3 marks]C
Real-world Applications
Answer all questions. Show your reasoning clearly.
1.
A company tests two machines. Machine A has a 95% success rate and Machine B has an 88% success rate. If a product is made by choosing a machine at random (equal probability), what is the probability that the product is successfully made if both machines are used independently?
[3 marks]2.
A health survey indicates 10% of people have a certain condition. The test correctly identifies the condition 90% of the time, but also has a 5% false positive rate. If a person tests positive, what is the probability they truly have the condition?
[4 marks]D
Challenge & Extension
Answer all questions. Provide detailed calculations where necessary.
1.
In a game, the probability of winning is 0.6, and the probability of losing is 0.4. If three independent games are played, what is the probability of winning exactly two games?
[3 marks]2.
A company has two machines, each with independent probabilities of producing a defective item: 0.02 and 0.03 respectively. If one item is produced by randomly choosing a machine, what is the probability that the item is non-defective?
[3 marks]E
Error Analysis
Below are common mistakes made in multiplying probabilities along branches. Review and correct the errors.
1.
A student multiplies the probabilities of two events as 0.5 × 0.5 = 0.25. Is this correct? Explain and correct if necessary.
[2 marks]2.
A student incorrectly adds probabilities instead of multiplying: 0.4 + 0.3 = 0.7. Why is this wrong when calculating joint probability?
[2 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet