TMUA Probability and Counting
TMUA does test probability, though not in as much depth as other college entrance exams. However a good understanding of general probability and counting techniques is useful. We also include here Venn Diagram questions and other tabular methods of arranging data to extract probabilities more simply.
For those so interested, we offer both one to one TMUA coaching on probability and counting, as well as online group coaching via Zoom - 'TMUA Statistics and Probability' is Session #13 of 20. Check our TMUA Group Coaching Schedule page for dates when these sessions are available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our 'Online Coaching FAQ'.
Feel free to contact us if you require more information regarding any of the above.
Free Revision Resources
The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions on probability and counting - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.
- Teaser #61 - tests basic understanding of Venn Diagrams given probabilities - Mild
- Teaser #119 - tests ability to count Andy's socks - Fairly Mild
- Teaser #375 - tests ability to calculate basic probabilities in a 'balls in bag' game - Standard
- Teaser #82 - tests understanding of probability that a result is a false positive - Standard
- Teaser #423 - tests how to find the number of perfect square factors (ie products of even powers) of 162,000 - Standard
- Teaser #241 - tests how to calculate minimum value of P(A or B) - Standard
- Teaser #97 - tests understanding of probability two balls picked are different colours given ratios of balls in bag - Standard
- Teaser #62 - tests calculating probability of false positive at a Taylor Swift concert - Standard
- Teaser #70 - tests ability to calculate expected throws of one dice before two consecutive sixes - Standard
- Teaser #78 - tests ability to work out probabilities in a fairground game - Standard
- Teaser #169 - tests probability only one component in a circuit fails - Standard
- Teaser #9 - tests ability to count number of ways of arranging people in a circle given constraints - Standard
- Teaser #109 - tests ability to find probability a girl sits between her friends - Standard
- Teaser #93 - tests finding expected score on a dartboard based on probability of landing in certain areas - Medium
- Teaser #155 - tests how many ways to arrange 3 families of 4 at the cinema - Medium
- Teaser #160 - tests knowledge of calculating P('A|'B) using Venn Diagram - Medium
- Teaser #256 - tests knowledge of probability of independent events - Medium
- Teaser #101 - tests counting arrangements of a word with restrictions - Medium
- Teaser #238 - tests ability to solve a board based maths coin placing counting puzzle - Medium
- Teaser #63 - tests ability to count number of integer solutions to xyz=360 - Medium
- Teaser #220 - test how to calculate probability exactly 2 people from 10 have a birthday today (calculation too hard for TMUA but method useful) - Medium
- Teaser #81 - tests ability to extract information and put on Venn Diagram and solve - Medium
- Teaser #226 - tests counting expected number of cards turned over before second spade - Medium
- Teaser #46 - tests understanding of various dice throwing probabilities - Medium
- Teaser #49 - tests ability to understand coin toss probabilities in a game - Medium
- Weekend Workout #20 - tests knowledge of permutations and the probability that balls are in a certain order - Medium
- Teaser #399 - tests ability to extract relevant information from the problem given, and thus calculate a probability that a random member is a female golfer - Medium
- Teaser #370 - tests ability to extract relevant information from the problem given, and thus calculate a probability that a random member is a male tennis player - Medium
- Weekend Workout #17 - tests counting the number of ways of splitting prime factors of a number into other numbers - Medium
- Teaser #331 - tests ability to enter data into a Venn Diagram and work out a probability using basic combinatorics - Medium
TMUA Past Questions on Probability and Counting: SP p1 q7; SP p2 q13; 2016 p1 q7; 2019 p2 q9; 2019 p2 q12; 2021 p2 q3; 2022 p1 q19; 2023 p1 q18
Practice makes perfect - good luck in your studies!