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## 'The Derren Brown Coin Flipping Scam' printed from http://nrich.maths.org/

The illusionist Derren Brown famously flipped a coin continuously
on camera until he obtained 10 heads in a row. He then simply
showed the last 10 flips of the film on TV, claiming that he
influenced the outcome of each flip to get 10 heads first
time.

Lots of ideas concerning risk and probability enter into this scam,
and it is great for discussion. Why not consider these short
questions as starting points? You will need to quantify carefully
any aspects which seem vague or unclear.

1. What was the chance of DB completing the coin scam on the first
attempt?

2. How many flips would you expect DB to have made before making
10 consecutive heads?

3. I've tried to repeat the DB coin experiment and have flipped my
coin 5000 times with no run of 10 heads and just got another tail.
How many more flips do I expect to need to make to make 10
consecutive heads?

4. My friend wants to replicate the coin flipping scam. How much
time should she put aside to be reasonably confident of completing
the challenge?

5. I've been flipping coins all day without success. I've just got
a tail and there is 10 minutes of the school day left. If I make 1
flip per second, what chance have I got of achieving the 10
consecutive Heads before the end of the day?

6. My friend in the Technology department has worked out a way of
slightly doctoring the coin to give a 55% chance of heads on each
throw instead of 50%. How helpful will this small change in
probabilities be to our chances of success?

7. What physical effects might bias the results or affect the
outcome?

8. DB took about 10 hours to get the 10 heads in succession, which
was longer than might be expected. How unlucky was he to have taken
this long? Very unlucky? Quite unlucky? How might you quantify this
statement?

9. Suppose that everyone in Britain flipped a coin until they
obtained 10 consecutive heads. What range would you estimate the
shortest number of flips to be. How about for the longest number of
flips?

10. Imagine that someone wanted to try to replicate this stunt,
only this time stopping with a greater number of consecutive heads.
For what number of consecutive heads would this be practically
feasible?