UCAT Probabilistic Reasoning Practice Questions, Tips & Techniques

Advice & Insight From UCAT Specialists

Probabilistic reasoning questions make up a part of the decision-making section in the UCAT. In this article I will outline how to tackle these questions.
Although most of the decision-making section of the UCAT may seem quite unfamiliar, probabilistic reasoning is a part of it that may be very similar to the probability questions that you did in your maths lessons at school. 

Rules of Probability

These are the general rules to refresh your memory. I am not going to go into these in a lot of detail so if you need a detailed refresher revisit the probability topic from GCSE maths.

1) The probabilities of all the outcomes of a single situation must add up to 1 (or 100%). So, if the probability of rain is 0.4. The chance of no rain must be 0.6 because 1-0.4=0.6.  

2) Probability trees can aid you when calculating the probability of multiple situations occurring. However, for time’s sake, try and determine if you can solve the question without one, this will come with practice.  A probability tree would be a good idea when dealing with multiple dice throws. The one below can be used to calculate the probability of rolling even or odd numbers in two dice roles. The probability of throwing even in one throw is 3/6 which is 1/2. This is the same for odd. 

3) AND rule: If you need to work out the probability of situation a AND situation b occurring, multiply both the probabilities. E.g. What is the probability of rolling two Evens? The question is asking what the probability is for rolling an even number on the first roll AND even on the second roll. 

4) OR rule: If you need to work out the probability of situation a occurring OR situation b occurring, add the probabilities of a and b. E.g. What is the probability of rolling an odd and an even? At first this question may seem like just an AND question. As AND is involved so you have to multiply. However, OR is also involved. In other words, what is the probability of rolling an even and an odd OR an odd and an even?

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UCAT Probabilistic Reasoning Practice Questions

Now I will do 2 worked examples of questions provided by the UCAT Consortium in the free UCAT test A. Try to work through the questions yourself before looking at the solution. 

​Read the question and try to understand what it is asking you. For this question you must determine if the probability of the coin landing on heads is still p on the 11th throw. 
It may be tempting to draw a probability tree for the previous 10 throws, but not only is that a waste of time, it is not going to help. Remember when we talked about probability trees above, we said use them when there are multiple situations occurring. This question is trying to trick you by saying it is the 11th throw. The previous 10 throws actually do not matter as it is only talking about that specific throw; the previous throws do not change the properties of the coin to change the probability of it landing on heads.  Therefore, it follows that the probability of the coin landing on Heads on the 11th throw will still be p. (It would be different if the question was referring to the probability for the coin landing on p on all 11 throws, which would involve the AND rule: it will be P to the power of 11)
A – Is correct. Look at the paragraph above.
B – It doesn’t matter if p is greater than half, equal to half or even less than half. It doesn’t change the fact that the probability of landing a head will always be P, unless the shape of the coin somehow changed making it more or less biased to landing a head.
C – Again, the value of p doesn’t really matter.
D – Probability is not exact; it is just an estimate/ likelihood of something happening based on factors. Therefore, just because the probability is p doesn’t actually mean that the proportion of actual throws will completely represent that. E.g. If the probability of it raining was constantly 0.2 for the next 10 day, it doesn’t necessarily mean only 2 days out the 10 will be rainy days.

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Firstly, read the question and skim through the answers. You don’t need a tree diagram for this as you don’t actually need to work out the answers and the values are easy to work with. The question states that in both hospitals there is a one in ten chance of useable machines breaking down (2/20 = 1/10). You can then work out that in hospital A, 98% of the machines are useable (100-2 =98), which is greater than the 75% in hospital B so answer D is correct.

However, if you had to work out the actual values or you just want a visual representation of the question, there are two probability trees below for hospital A and hospital B with all the relevant information to work out which hospital is better. This is an AND situation: useable machine AND no break down. 

Hopefully, this article has made things clearer. Remember practice will make perfect and ensure you do not panic if you’re having difficulty with a question– flag and review!

UCAT Probabilistic Reasoning Practice Questions, Tips & Techniques

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