Can't find a coin?
Problem
How will you go about 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!
Getting Started
How often do you expect the result from a throw to be the same as the result from the previous throw?
How often do you expect to get a run of three identical results?
How often do you expect to get a run of four identical results?
How often do you expect to get a run of five identical results?...
Student Solutions
Nabeelah from Langley Grammar School commented that:
Some people suggested ways in which to get results that appeared likely.
Eloi fromSt. Patrick's Catholic Primary School went about it like this:
Thomas from High Storrs suggested this:
The best way of making the results seem random is not having equal numbers of heads and tails. If you decide to have more heads then have large groups of heads with a few tails in between in groups of three. If you alter the size of the groups of heads then the results appear random.
Philippa from Ashcroft Academy worked
out that Earl had the most suspicious results:
I think Earl is the cheat because his heads and tails are pretty
much equal as if he tried too hard to simulate the random pattern
of a coin.
Another way of telling that Earl is the most likely cheat is to notice that he has no strings of repeated results of length of 5 or more, and when you realise that there are 95 strings of 6 consecutive results (1st, 2nd, 3rd, 4th, 5th and 6th - 2nd, 3rd, 4th, 5th, 6th and 7th - 3rd, 4th, 5th, 6th, 7th and 8th...) you may find it suspicious that long strings of repeated results do not appear at all.