Stage: 3 Challenge Level: 
Imagine your teacher has set you the homework task of throwing a
coin 100 times and carefully recording your results in the order
that they appear. Imagine that you can't be bothered to go and
find a coin - the task is just too tedious. So you decide to try
to fool your teacher.
How will you go about it?
If you have managed to fool the teacher twice in a row, tell us how you did it.
One of these students made up their homework results, which one is the most suspicious?
BACKGROUND INFORMATION
Whilst all combinations of Heads and Tails are equally likely, certain sets of results (such as all heads or alternating Heads and Tails all the way) would look rather suspicious. Why is this?
The computer here is programmed to determine whether the set of Heads and Tails falls into a suspicious category or not. Rather interestingly, if you do generate the Heads and Tails truly randomly using a coin then there is a 95% chance the the computer will know that these were generated randomly. Don't believe it? Try it out!
How will you go about it?
This text is usually replaced by the Flash movie.
If you have managed to fool the teacher twice in a row, tell us how you did it.
One of these students made up their homework results, which one is the most suspicious?
BACKGROUND INFORMATION
Whilst all combinations of Heads and Tails are equally likely, certain sets of results (such as all heads or alternating Heads and Tails all the way) would look rather suspicious. Why is this?
The computer here is programmed to determine whether the set of Heads and Tails falls into a suspicious category or not. Rather interestingly, if you do generate the Heads and Tails truly randomly using a coin then there is a 95% chance the the computer will know that these were generated randomly. Don't believe it? Try it out!
Conditional probability. Tree diagrams. Permutations. Experimental probability. Combining probabilities. Equally likely outcomes. Probability. Interactivities. Combinations. Theoretical probability.
Published June 2008.
Copyright © 2007. University of Cambridge. All rights reserved.
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email: nrich@damtp.cam.ac.uk
