Year 11 - Maths
Conditional probability in a tree diagram
Conditional probability
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils use their knowledge of calculating theoretical probabilities and extend it to calculate conditional probabilities.
Lesson Summary
You will learn to calculate a conditional probability from a tree diagram.
Key Notes
- A tree diagram can be used to calculate conditional probabilities
- A tree diagram can be used to calculate conditional probabilities involving sets of events
- Tree diagrams allow us to identify which events are mutually exclusive
- Tree diagrams can be used to identify which events are independent
Vocabulary To Learn
- Probability: The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.
- Probability tree: Each branch of a probability tree shows a possible outcome from an event or from a stage of a trial, along with the probability of that outcome happening.
- Independent events: Event A is independent of event B if the probability of event A occurring is not affected by whether or not event B occurs.
- Mutually exclusive: Mutually exclusive events have no outcomes in common.
Common Mistakes To Avoid
- When pupils construct probability trees for scenarios where two marbles are removed from a bag, they may mistakenly subtract 2 from the denominators of the probabilities instead of 1.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A tree diagram can be used to calculate conditional probabilities. A tree diagram can be used to calculate conditional probabilities involving sets of events.
2. Use this key word in a maths sentence and explain it clearly. 'Probability'
The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When pupils construct probability trees for scenarios where two marbles are removed from a bag, they may mistakenly subtract 2 from the denominators of the probabilities instead of 1. Correction: Even though two marbles are removed from the bag at once, you can think of it at choosing one marble and then immediately choosing a second marble. At the end of the process, two marbles have been removed.
More Lessons In This Unit
- Advanced problem solving with conditional probability Study Guide
- Algebra in tree and Venn diagrams Study Guide
- Checking and securing calculating probabilities from diagrams Study Guide
- Checking and securing calculating probabilities from tables Study Guide
- Checking and securing displaying outcomes Study Guide
- Checking and securing exhaustive events Study Guide
- Combinations Study Guide
- Comparing multiple representations to calculate conditional probabilities Study Guide
- Conditional probability in a two-way table Study Guide
- Conditional probability in a Venn diagram Study Guide
- Constructing three event Venn diagrams Study Guide
- Experimental probability Study Guide
- Experimental vs theoretical probability Study Guide
- Frequency trees Study Guide
- Probabilities in three event Venn diagrams Study Guide
- Probabilities involving algebra Study Guide
- Problem solving with conditional probability Study Guide
- Set notation Study Guide
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