Stage: 3 Challenge Level:
Ed from St Peter's College started off by
experimenting and gave an initial insight into the
I flipped a coin 20 times and got the following results: 13 heads
and 7 tails. The best way to analyse if the coin is real or not is
whether it has a significant number more of one side over the
Krystof from Uhelny Trh, Prague gave
examples of some of his runs:
I made three runs
Number 1 is real, there are not exactly the same number of heads
and tails, but nearly. There are also lots of different length
runs, but mostly 2s and 3s.
Numbers 2 and 3 are made up. They have regular patterns. There is a
very small probability of these occuring randomly.
There are many interesting principles of
probability and statistics revealed in this simple activity. Connor
from Gladesmore gave some very good points:
For a total random coin the number of "runs" of heads/ tails should
be more weighted toward the smaller runs. Also a table where the
result alternates e.g. h, t, h, t will be more likely the fake one
as although the total number of heads and tails should be almost
the same the order should be random. Finally when there are only a
small number of coins flipped then you would expect that the total
will not be completely identical.
Good job everyone! Can anyone add more?
What about the probability of different length runs