Are You Psychic?

Luke Brooke

Are you psychic? That was a question asked to every maths scholar at our most recent CPD workshop. Some people answered yes, some no, and some were just really excited to see what area of maths we were about to dive into in order to explore this question. 

It began with the introduction to the challenge. There are five cards, with five different symbols and you, as the potential psychic have to look into the mind of whoever holds the cards and show off your psychic skills! 

No one got a perfect score. 

So did this mean that we had no psychics here and should move on? No, in fact this is where the maths got interesting. We were asked what would the threshold of a score be where there would be some evidence that you could be psychic, and how could we decide on this threshold? 

Lets get specific. There were five cards to choose from, and we ran 5 trials in each run in our test for psychic ability. That would mean if we were randomly guessing, we would have a 1/5 chance to get a card correct on each trial, so starting simple we could find the probability of getting every card correct if you don't have a psychic gift. It would be a 1/5 chance for each trail, so a total probability of 1/5*1/5*1/5*1/5*1/5 which has a probability of 0.032%, so we're pretty sure if someone did that then some further studies into their mind could be warranted! But what if they instead got four correct? Would that be just as impressive? Now finding the probability wouldn't be quite so straight forward, since the card they got wrong could have been the first, or the second, or the third, etc. There are different options to consider to find our overall probability, and this is where the underlying maths really starts to show itself! We have been looking at a binomial distribution. We continued our investigation by counting the different combinations for four cards correct and for three, two, one, and even getting zero cards correct so we could see the complete collection of probabilities, and then asked to consider what result would lend enough evidence to reject our assumption that you were just guessing and that the probability of getting it correct was 1/5. We decided that finding four cards correct would be where we would start to look at the ""guess"" with a bit more intrigue. 

This was an incredible session to take the role of the student being introduced in stages to some really interesting and rather complex maths. It reminded me again that there's often away to introduce to topic to students, that could have been really dull for them, with instead a collaborative investigation into an interesting question that would get them excited. A question like: Are you psychic?

By Luke Brooke  

Image supplied by the author. 

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