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Dependence of events, revisited

Published online by Cambridge University Press:  23 August 2024

Peter Braza
Peter Braza*
Affiliation:
University of Colorado, Colorado Springs, 1420 Austin Bluffs Road, Colorado Springs, CO 80918 USA e-mail: pbraza@uccs.edu
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Extract

Independence is a key concept in probability. Conceptually, we think of two events as being independent if the outcome of one event doesn’t affect the outcome of the other and vice versa. Mathematically, we say that events A and B are independent if the probability that both occur is the product of the probabilities that each occurs. More precisely, P (A ∩ B) = P (A) (P (B) in which P () denotes the probability of the given event. Alternatively, we say that A and B are independent if the conditional probability that A occurs given that B has occurred, P (A | B), satisfies P (A | B) = P (A). That is, whether or not B occurs does not affect whether or not A occurs.

Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 572 , July 2024 , pp. 257 - 261
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Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

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