# Introduction to Artificial Intelligence (ARIN)

## Probability Practical

#### The red and the green

Suppose I have three cards. One card is green on both sides, one is red on both sides and one is red on one side and green on the other. Suppose I select a card at random and then choose one side of that card to show you, also at random. If the side you see is red, then clearly the card is either the one with both red sides or the one with sides of different colours. What is the probability that the other side is also red?

A doctor wishes to test one of his/her patients for Blogg's disease which afflicts one person in every 1000. There is a well-developed test for the occurrence of Blogg's disease, so that

• if an individual has Blogg's disease the probability of a positive test result is 0.95
• if an individual does not have Blogg's the probability of a positive test result is 0.01

The patient gets a positive test result. How likely is it that he/she has Blogg's disease?

#### Winning prizes

We haven't "covered" this sort of topic in the module - this is just a test of your probabilistic intuition. There's a game show in the US where a prize is hidden behind one of three curtains. Firstly, the contestant chooses one of these curtains. Let's call this curtain A. At this point, at least one of the other curtains, let's call them B and C, does not have a prize behind it. The host then selects one curtain other than the one chosen, and shows the contestant that there is no prize behind it. If the host has a choice of curtains he chooses one at random. Suppose B were the chosen curtain. The contestant can now either stick with their initial guess (A) or switch to the remaining curtain (C). Which should they do to maximise their probability of winning the prize? What are the probabilities of winning the prize with the two strategies?