Mathematics: Skills & Insight – Probability Paradoxes With Dr Audrey Kueh From University of Surrey

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In this Mathematics session, Dr Audrey Kueh, a leading academic from University of Surrey, will run an interactive skills and insight workshop for students on Probability Paradoxes.

We consider the following three problems:

• There are three boxes. One box has 2 gold coins, one box has 2 silver coins and one box has a gold coin and a silver coin. A box is chosen at random, and one of the two coins in that box is removed at random. Given the removed coin is gold, what is the probability that the other coin in the chosen box is gold?
• Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1. The host then selects one of the doors with a goat from the remaining two doors, say No. 2, and shows you the goat behind that door. He then says to you, “Do you want to pick door No. 3?” Is it to your advantage to switch your choice?
• Jørgen wants a pet iguana. Only 1% of the population is allergic, but he takes a test to be sure. The test has an error rate of 10%: 90% of allergic people who take the test return a true positive result, whereas 10% of non-allergic people who take the test return a false positive result. Given he tests positive, what is the probability that he is actually allergic?

In this seminar, we will first do a poll to see what you think are the correct answers to the three problems. Then we will recap tree diagrams and conditional probability, considering simple problems. We would then reconsider the problems and show how you can get the right answers, if you haven’t managed already!

Lecturer Profile (Please Click): Dr Audrey Kueh

Our events are designed so that a group of students can take part from a classroom or students and teachers can take part as individuals, either from school or from home. This means that sessions will continue irrespective of possible school closures.

As a live, participative event, this session will not be recorded but slides and other resources will be shared after the event, where available.

Suitable for: KS5 students (and equivalent) studying, or with a possible interest in studying, Mathematics and related disciplines.

Preparation/Pre-Reading: Please attempt the three problems in advance and have your answers ready at the start of the session. Students can also think about questions they have about studying Mathematics at university level.

The IT Setup: The event will be run on Bluejeans (similar to Zoom) and participants will be able to join using laptops, tablets, and mobile devices. If you are joining as a school group, we recommend connecting with one device and projecting on to a whiteboard. You will be able to interact with the university via a microphone and/or typed comments and questions. Full details will be sent to those who have registered (see below) prior to the event.

Booking a Place: This is free for schools and colleges. If you would like to take part in this event, please register your interest using the link to the registration form below:

Register here