Probability Question challenges

Keep an eye out for Probability questions that are simply about forming two probabilities and comparing their values.

These questions can be quick work once you have a bit of practice.

Aim to answer such questions in 30 seconds or less. If you are more experienced and confident, push yourself to go faster – try for 15 seconds or less.

A Probability question might ask you to compare two options using two criteria.

Most commonly, the two options are described with letters, such as:

• Robot A and Robot B
• Vaccine J and Vaccine K
• Advertisement X and Advertisement Y

The criteria could be any type of number, but the question will almost always present them as independent of each other for each option. Examples include:

• charging time and success rate (for Robots A and B)
• uptake rate and efficacy rate (for Vaccines J and K)
• whether people liked the advert and whether they purchased the product (for Advertisements X and Y)

For each criterion for each option, the sum of all possible outcomes is 100%.

Notice that in most official questions like this, each criterion for each option will have outcomes in two components. For example: Success Rate + Failure Rate = 100%.

In the official UCAT practice materials, it’s a lot more common to see two options with two criteria than any harder variations. But let’s consider how the UCAT could increase difficulty and make you work a bit more intensely in these Probability questions.

In the common format, each criterion for each option has outcomes in two components, such as a success rate and a failure rate, or customers who bought the product and customers who didn’t buy the product.

In the rarer, harder formats, you will usually see outcomes divided into three or four components. Each component could be:

• an exact number – whether given as a percentage (between 0% and 100%) or a fraction or decimal (between 0 and 1), or
• a range of values that, taken together, add up to 1 (if all converted to fractions or decimals) or 100% (if all converted to percentages).

As a further twist, in the rarer, harder format with three or four components:

• Usually, you will find two options to select between.
• There may be just one criterion that is divided into three or four components.

Thus, there will likely be more numbers and also more elaborate phrasing with the additional components.

But ironically, your task is rather more straightforward. You will generally have to:

• Subtract the provided values (decimals or fractions) from 1, or
• Subtract the provided values (percentages) from 100%.

The correct answer will usually involve one component whose value (as a decimal, fraction or percentage) is not provided, but can be found if you subtract the other possibilities from the sum of all possibilities.

Probability questions could include almost any format or challenge, but it is not worth worrying about what is theoretically possible. Focus on what is common and expected, based on the official practice materials.

At the same time, you can minimise stress by being aware of other formats that are quite rare. As a result, you will have limited practice since there are so few examples in these other formats.

But the other formats are useful in understanding the boundaries of the logic and maths required in most Probability questions. The maths concepts are generally fairly simple, so you can avoid intensive revision of more complicated concepts.

You are very unlikely to need the permutation or combination formulae in UCAT Decision Making. We have never seen an official question that requires them.

More likely, you might need to apply simple counting and logic to consider the possible outcomes that fit the terms of the question.

This could be as basic as listing the outcomes in your head, on scrap paper or in your notebook on Test Day. You could also use the product rule for counting to find the total number of different combinations of multiple options or events.

Remember that any outcome that already happened should not be included in a probability fraction or calculation, since you know the outcome of that event.

You could possibly see a Probability question focusing on concepts from statistics rather than the more common probability topics that are involved in virtually all of the official practice questions.

Over the years, there have only been a couple of official practice questions that involve other topics from statistics without touching on probability at all. Thus, you are highly unlikely to see any such questions on Test Day, but they are theoretically possible.

If a question’s focus is statistics without probability, be ready to apply some basic principles:

• A survey or study should ideally use random sampling from the population being studied.
• The sample size of a survey or study could simply be too small.
• A survey or study may be faulty due to sampling bias if part of the population makes up too large or too small a part of the data, which could significantly skew the results or interpretation of the results.
• The wording of a survey – or other factors in its approach to data collection – could be biased, or could result in inaccurate or unreliable data.

Across these various principles, the key problem is one of representativeness. There is likely to be something in the survey or study that makes its conclusion inaccurate or unreliable, either:

• according to the question it posed, or
• in terms of the population it purports to represent.

We think it is extremely unlikely you would need to know any more advanced concepts related to statistical analysis, such as modules you might have covered in A-level maths or other higher-level maths curriculum. This is almost certainly beyond the level of the UCAT.

If you see a DM question about statistics but not probability, ask yourself: Is the survey or study representative? What about the survey or study – or its conclusions – suggests it is unrepresentative?

You might see a Probability question with visual data, such as a table, chart or graph.

Whilst there are only a handful of such questions in the official UCAT practice materials, they have become a bit more prevalent in recent years. Even so, it’s mostly likely you’d see one or none of such questions – but they are more likely to appear on Test Day than the ones with combinations or other statistical concepts noted above.

Take a bit of time to practise using visual data in Probability questions, so you’ll be ready if it appears on Test Day.

The big difference when you see visual data in a Probability question is that there are more numerical values you might need to solve the question.

With a graph or chart, see if you might need to simply select some numbers to use in your rough working.

With a table, you may need to sum up rows or columns, or you might have to calculate a probability fraction or percentage for each row or column.