Abstract
If statistics can be defined as the science that studies uncertainty, then probability is the branch of mathematics that quantifies it. One’s intuition of chance and probability develops at a very early age (Piaget and Inhelder, 1976). However, the formal, precise definition of probability is elusive. There are several competing definitions for the probability of an event, but the most practical one uses its relative frequency in a potentially infinite series of experiments.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Chapter References
Adel, A. L., Dorr, R. T., Liddil, J. D. (1993). The effect of anticancer drug sequence in experimental combination chemotherapy. Cancer Invest., 11, 1, 15–24.
Barbeau, E. (1993). The problem of the car and goats. College Math. J., 24, 2, 149–154.
Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philos. Trans. R. Soc. Lond., 53, 370–418.
Bonferroni, C. E. (1937). Teoria statistica delle classi e calcolo delle probabilita. In Volume in Onore di Ricarrdo dalla Volta, Universita di Firenza, 1–62.
Casscells, W., Schoenberger, A., and Grayboys, T. (1978). Interpretation by physicians of clinical laboratory results. New Engl. J. Med., 299, 999–1000.
Gillman, L. (1992). The car and the goats, Am. Math. Mon., 99, 1, 3–7.
Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer, Berlin.
Laplace P. S. (1774). Mémoire sur la probabilité des causes par les évenements. Mém. De l’Ac. R. des Sciences de Paris, 6, 621–656.
Lauritzen, S. L. and Spiegelhalter, D. L. (1988). Local computations with probabilities on graphical structures and their application to expert systems. J. R. Stat. Soc. B, 50, 157–194.
Piaget, J. and Inhelder B. (1976). The Origin of the Idea of Chance in Children. W.W. Norton & Comp., NY, 276 pp.
Ross, S. (2009). A First Course in Probability, 8th Edition. Prentice Hall.
Selvin, S. (1975). A Problem in Probability. Am. Stat., 29, 1, 67.
Venn, J. (1880). On the employment of geometrical diagrams for the sensible representation of logical propositions. Proc. Cambridge Philos. Soc., 4, 47–59.
Wong, S. K. N., O’Connell, M., Wisdom, J. A., and Dai, H. (2005). Carbon nanotubes as multifunctional biological transporters and near-infrared agents for selective cancer cell destruction. Proc. Natl. Acad. Sci., 102, 11600–11605.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Vidakovic, B. (2011). Probability, Conditional Probability, and Bayes’ Rule. In: Statistics for Bioengineering Sciences. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0394-4_3
Download citation
DOI: https://doi.org/10.1007/978-1-4614-0394-4_3
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-0393-7
Online ISBN: 978-1-4614-0394-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)