WeSolve+ reads the whole document and writes the questions for you
Upload your PDF, photograph your notebook, or point the camera. WeSolve+ writes questions from that material, explains why each answer is right, reads the chapter back to you as a podcast, and remembers every item you missed until you own it.
The tool below is a small browser-only tool and it is not WeSolve+: paste a few lines and text rules turn them into cards on the spot. The real app, the one that uses AI, is behind the link above.
Probability rules, from your notes
This is a browser-only tool, and that is all it isIt splits the text you paste by rule, and nothing else. WeSolve+ is a different thing entirely: it reads your whole PDF with AI, writes the reasoning behind every question, speaks the chapter back to you, and remembers what you missed so it can return it. Try the real app now, free!
This tool splits the text you paste by rule and returns cards. It cannot compute a probability, so it works on the rules you already wrote down.
Independent and mutually exclusive are opposites, not synonyms
Independent means knowing one happened tells you nothing about the other. Mutually exclusive means knowing one happened tells you the other definitely did not, which is the strongest possible dependence. Two events with non zero probability cannot be both, and questions test exactly that confusion.
The word given changes the denominator
Conditional probability restricts attention to a smaller world: the cases where the condition holds. Once you see the word given as an instruction to shrink the denominator, most conditional questions become arithmetic. Students who treat it as a phrasing detail get plausible and wrong answers.
Expected value is a long run average, not a prediction
It can be a number the random variable never takes, such as an average family size of two point four children. Answers that treat it as what will happen next misunderstand what was computed, and questions include impossible expected values deliberately to test this.
Check the binomial conditions before using the formula
A fixed number of trials, independence between them, the same probability each time, and two outcomes. If sampling without replacement from a small population, independence fails and the binomial model is not appropriate. Naming the failed condition is worth more than computing the wrong number carefully.
Simulation is a legitimate method here, not a fallback
Describing how you would simulate a situation, including how you assign digits and what counts as a success, is an examinable skill in its own right. It also builds the intuition that computation alone does not, because you have to state the model explicitly before you can imitate it.
What to photograph for Probability and Random Variables
Your worked problems with the context sentences left intact. Related: Unit 1, PDF to quiz and pricing.
Sources used on this page
- College Board, AP Statistics
- Probability
- Random variable
- Probability distribution
- Binomial distribution
- Active recall
- Spaced repetition
- Testing effect
- Forgetting curve
- Generation effect
- Judgment of learning
- Metacognition
- Desirable difficulty
- Distributed practice
- Formative assessment
- Flashcard
- Cloze test
- Multiple choice
- Test (assessment)
- Educational assessment
- Advanced Placement
- Curriculum
- Study skills
- Study guide
- Note-taking
- Overlearning
- Instructional scaffolding
- Item analysis
- Mastery learning
| Situation | Ask this | Common error |
|---|---|---|
| Two events described | Independent or exclusive | Treating them as the same |
| The word given appears | Which cases remain | Using the full denominator |
| An average is requested | Long run or next trial | Reading it as a prediction |
| Repeated trials | Are the four conditions met | Applying binomial regardless |
| Sampling without replacement | Is independence broken | Ignoring the population size |
| A model is unclear | Could I simulate it | Guessing a formula |
What is AP Statistics Unit 2?
Probability, Random Variables and Probability Distributions: the rules of probability, conditional probability, expected value and the binomial and geometric settings.
What is the difference between independent and mutually exclusive?
They are opposites. Independent means one tells you nothing about the other; mutually exclusive means one tells you the other did not happen.
How do I handle the word given?
As an instruction to shrink the denominator to the cases where the condition holds. Most conditional questions become arithmetic once you do.
Can an expected value be impossible?
Yes, and questions use that deliberately. It is a long run average, so an average family size of two point four is normal rather than an error.
When can I use the binomial model?
With a fixed number of independent trials, the same probability of success each time, and two outcomes. Sampling without replacement from a small population breaks independence.
Is simulation actually examinable?
Yes. Describing how you would assign digits and what counts as a success is a skill in its own right, and it forces the model into the open.
Last updated: 2026-08-15