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parallel to edges of the rectangle; if the part to the left of the vertical line is labelled A and the part above the horizontal one B (for example), the diagram would nicely show independence since the areas within it would be in the right proportion. The proportion of A's area that also lies within B's area would indeed by the same as the proportion of Ω's area that lies within B's; and conversely. -- Eddy.
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Fixing the upper half's label would indeed illustrate the difference between mutually exclusive and the alternative, but its name claims it illustrates independence and its alternative. The latter would be better described by an image showing the available space Ω as a rectangle, divided by two lines
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displayed alongside discussion of
Mutually Exclusive and Independent events is mislabelled and misnamed. The lower portion of the image shows two outcomes that overlap and is correctly labelled as showing non-mutually-exclusive events. However, above it, a pair of mutually-exclusive events are
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I feel that this page would be clearer if it contained a distinction between the branches of probability termed aleatory (of future events that haven't unfolded yet) and epistemic (resulting from insufficient knowledge). While the mathematics is the same, the implications are quite
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The person who wrote up odds as currently displayed on the page got it wrong. A 2:1 event is not an event with probability 2/3; it is a 1/3 probability event. The formula a/(a+b) needs to be replaced with b/(a+b) and is probably best illustrated with a reference to gambling.
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labelled as independent, which they are not (unless one of them has probability zero), since it shows p(A and B) = 0 (they are mutually exclusive) and, for this to be p(A).p(B), one of p(A) and p(B) must be zero. So the diagram is mis-labelled.
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I submit that the memoir De erroribus (1823) by C F Gauss should be mentioned. Gauss derives the error functgon connected with his name, from only three assumptions.
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Error in image illustrating
Exclusive-or-not events
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