DM: Probabilistic Reasoning & Statistics
Probabilistic Reasoning in the UCAT
These questions test your ability to interpret statistical information and make sound judgements about likelihood. You do NOT need advanced statistics knowledge — the questions test logical reasoning about probability, not calculation.
Key Concepts
1. Base Rate Neglect
This is the most common trap. Consider: “A disease affects 1 in 1000 people. A test for the disease has a 99% accuracy rate. If a person tests positive, what is the probability they actually have the disease?”
Most people say 99%, but the correct answer is approximately 9%. This is because the 1% false positive rate applied to 999 healthy people (~10 false positives) outnumbers the ~1 true positive. Always consider the base rate (prevalence) when evaluating test results.
2. Conditional Probability
P(A|B) — the probability of A given B — is NOT the same as P(B|A). “The probability of having a cough given you have a cold” is different from “the probability of having a cold given you have a cough.”
3. Correlation vs Causation
A strong correlation between two variables does NOT mean one causes the other. Always consider: reverse causation (B causes A instead of A causing B), confounding variables (C causes both A and B), and coincidence.
4. Sample Size and Representativeness
Small samples are less reliable. A study of 10 patients is far less conclusive than a study of 10,000. Also consider whether the sample is representative — a study conducted only in one hospital may not generalise to all hospitals.
Common Question Formats
- “Which of the following conclusions is best supported by this data?”
- “What is the strongest criticism of this study’s methodology?”
- “Which statement, if true, would most weaken this argument?”
- “What additional information would be most useful in evaluating this claim?”
Strategy
- Read the scenario carefully — identify what data is actually provided vs what is assumed
- Look for base rate information — if it’s missing, that’s often the key to the answer
- Be skeptical of causal claims — look for the correlation-vs-causation trap
- Check sample sizes and selection methods — small or biased samples weaken conclusions
- Evaluate what the data actually shows vs what the argument claims it shows