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‘Catch-up’ numbers

Published online by Cambridge University Press:  01 August 2016

Martin Griffiths
Martin Griffiths*
Affiliation:
Colchester County High School for Girls, Norman Way, Colchester, CO3 3US
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Extract

It never ceases to amaze me how often an apparently innocent-looking problem can lead on to something altogether more deep and interesting. As an example of this, I had recently set one of my Lower Sixth classes, as part of a statistics revision lesson, the task of devising some original questions on probability when the following problem emerged:

‘A person tosses a fair coin six times. Given that 4 heads and 2 tails result, what is the probability that the proportion of tails obtained at each point before the last toss is less than one third?’

Type
Articles
Information
The Mathematical Gazette , Volume 91 , Issue 522 , November 2007 , pp. 500 - 509
Copyright
Copyright © The Mathematical Association 2007

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References

1. Lobb, Andrew Deriving the nth Catalan number, Math. Gaz. 83 (March 1999) pp. 109–110.Google Scholar
2. Knuth, Donald E. The art of computer programming, Volume 1, Addison-Wesley (1968).Google Scholar
3. Hilton, P. Holton, D. Pederson, J. Mathematical vistas, from a room with many windows, Springer (2000).Google Scholar
4. http://www.research.att.com/cgi-bin/access.cgi/as/nias/sequences.Google Scholar