UCAT Probabilistic Reasoning: how to solve them
Probabilistic reasoning ask you to find the probability of a specific outcome based on a defined set of conditions. It’s a Decision Making question type built on a small toolkit of probability rules rather than heavy calculations.
What is a probabilistic reasoning question?
Probabilistic reasoning questions are usually framed as short scenarios with various likelihood of certain events happpening. While several themes may be explored (taking a ball, flipping a coin, drawing a card, etc.), its really the same type of reasoning being tested - once you've stripped a question down to what it's actually asking, it's just a matter of applying the right formula
Where probabilistic reasoning gets tricky is specific terminology that affect how probabilities are calculated (or what it is the question's really looking for). Learn these terminology well and every one of these questions are simple.
Replacement: whether an item is put back before the next draw.
Identify which of these (it could be none, some or all) are relevant to your question to determine the correct formula(s) you should be using.
A worked example
Think you’ve got what it takes? Give this one a shot!
A jar contains 5 lime sweets and 3 orange sweets. Two sweets are taken out at random, one after the other, and eaten, so the first is not put back.
What is the probability that both sweets are lime?
Common mistakes
Incorrect answers in probabilistic reasoning almost always come from not respecting the question's terminology. Here's a collection of the most common traps based on our assessment of past papers.
Trap guides are being published. Links open as each goes live.
A reliable method
Practising probability
Probability questions reward a small number of reusable moves (multiply or add, shrink the pool or not, flip to the complement), so the fastest progress comes from working through enough of them that you spot which move a scenario wants the moment you read it.
MedPath drills probabilistic reasoning trap by trap, with a worked, interactive solution for each, and steers your practice toward the traps you keep falling for.
Practise probability adaptively.
MedPath drills probabilistic reasoning trap by trap, with a worked interactive solution for each, and steers practice toward the traps you keep falling for.
Common questions
Do I need a calculator for probability questions?+
No. Decision Making gives you a simple on-screen calculator, but probability questions are written to be solved mentally — the sample space is small and the answer always simplifies to a clean fraction. If one seems to need a calculator, you’ve usually taken a longer route than intended.
How are probability questions scored?+
As part of Decision Making, they count towards its 300–900 scaled score. They’re single-best-answer, so — unlike the multi-statement Decision Making types — there’s no partial credit; you need the right fraction to earn the mark.
What’s the most common mistake?+
Treating draws “without replacement” as if the item were put back — keeping the pool the same instead of shrinking it — and adding two probabilities when the events should be multiplied.