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Concurrent sequences of Bernoulli trials

Published online by Cambridge University Press:  08 October 2020

Stephen Kaczkowski
Stephen Kaczkowski*
Affiliation:
South Carolina Governor's School, 401 Railroad Avenue, Hartsville, SC 29550 USA e-mail: kaczkowski@gssm.k12.sc.us
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Extract

Probability and expectation are two distinct measures, both of which can be used to indicate the likelihood of certain events. However, expectation values, which are often associated with waiting times for success, may, at times, speak more clearly and poignantly about the uncertainty of an event than a theoretical probability. To illustrate the point, suppose the probability of choosing a winning lottery ticket is 2.5 × 10−8. This information may not communicate the unlikely odds of winning as clearly as a statement like, “If five lottery tickets are purchased per day, the expected waiting time for a first win is about 22000 years.”

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The Mathematical Gazette , Volume 104 , Issue 561 , November 2020, pp. 435 - 448
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© Mathematical Association 2020

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References

Ferrante, M., Saltalamacchia, M., The coupon collector's problem. Materials matemàtics (2014) pp. 1–35.Google Scholar
Feller, W., An introduction to probability theory and its applications: Volume I, John Wiley & Sons (1968).Google Scholar
LeVeque, R. J., Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. Society for Industrial and Applied Mathematics (2007).Google Scholar
De Moivre, A., The doctrine of chances (3rd edn.) (1756), reprinted by New York: Chelsea Publishing Co. (1967).Google Scholar
Kennedy, S. F., Stafford, M. W., Coin flipping, dynamical systems, and the Fibonacci numbers, Math. Mag. 67(5) (1994) pp. 380–382.10.1080/0025570X.1994.11996257CrossRefGoogle Scholar
Griffiths, M., No consecutive heads Math. Gaz. 88 (November 2004) pp. 561–567.CrossRefGoogle Scholar
Rowland, T., Fibonacci, Toss!, Math. Gaz. 68 (October 1984) pp. 183–186.CrossRefGoogle Scholar
Howlett, G., Pargeter, A. R., Rindl, H., Wiseman, G., Consecutive heads and Fibonacci, Math. Gaz. 69 (October 1985) pp. 208–211.CrossRefGoogle Scholar
Griffiths, M., Fibonacci expressions arising from a coin-tossing scenario involving pairs of consecutive heads, Fibonacci Quart. 49 (2011) pp. 249–254.Google Scholar
Erdös, P., Rényi, A., On a new law of large numbers, J. Anal. Math. 23(1) (1970) pp. 103–111.CrossRefGoogle Scholar
Deheuvels, P., Devroye, L., Lynch, J., Exact convergence rate in the limit theorems of Erdös-Rényi and Shepp, Ann. Probab. 14 (1986) p. 20.CrossRefGoogle Scholar
Solov'ev, A. D., A combinatorial identity and its application to the problem concerning the first occurrence of a rare event, Theory Probab. Appl. 11(2) (1966) pp. 276–282.CrossRefGoogle Scholar
Baklizi, A., Approximating the tail probabilities of the longest run in a sequence of Bernoulli trials, Journal of Statistical Computation and Simulation 88(14) (2018) pp. 2751–2760.CrossRefGoogle Scholar
Schilling, M. F., The surprising predictability of long runs, Math. Mag. 85(2) (2012) pp. 141–149.CrossRefGoogle Scholar
Abramowitz, M., Stegun, I. A, Handbook of mathematical functions: with formulas, graphs, and mathematical tables, Applied mathematics series. Washington, DC: National Bureau of Standards (1964).Google Scholar
Borel, É., Mécanique statistique et irréversibilité, Journal de Physique, 5e série 3 (1913) pp. 189–196.Google Scholar