Pickles AcademyStart for freeTwo-stage experiments – practice for Year 9
Sample questions on Two-stage experiments with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.
- Subject
- Maths
- Year
- Year 9
- Curriculum area
- Relationships, functions and data
Question types: Tree diagrams · Two-way tables
Rule: Two-stage experiments
In a tree, multiply the probabilities along a path and add the probabilities of different paths.
Without replacement the second draw has one marble fewer: the bottom number changes, and maybe the top one.
Example: 3 red, 2 blue, without replacement: both red 3/5 × 2/4 = 6/20 = 3/10
Watch out: In a two-way table, divide by the total of the row or column the question is about.
Sample questions
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Question 1 Easy
A bag holds 4 red marbles and 3 blue marbles. We draw a marble at random, note its colour, put it back and draw again. What is the probability that the first is red and the second blue? Give the answer as a fraction in its simplest form.
Show the solution
Answer: 12/49How it works: 4/7 × 3/7 = 12/49
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Question 2 Normal
Zoo visitors were asked whether they bought an ice cream. The table shows the answers of adults and children. We pick one of the people asked at random. What is the probability that it is an adult who answered "yes"? Give the answer as a fraction in its simplest form.
Show the solution
Answer: 15/82How it works: 15/82
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Question 3 Hard
A bag holds 4 red marbles and 3 blue marbles. We draw one marble at random and then, without putting it back, a second one. Which probability belongs in the tree in place of the question mark? Give the answer as a fraction in its simplest form.
Show the solution
Answer: 1/2How it works: If the first is red, the second draw has 3 blue marbles out of 6: 3/6 = 1/2
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