Where P; is the probability of arrival in the "i" region; the total probability of occurrence is Pt = E P; = 2e-e2 ; and the required probability for this specific case is 11/36. This problem is equivalent to the one-dimensional unit probability collision case. (Note: if e « 1, the probability is approximately equal to 2e, i.e., the “edge/clipping” integrals are ignored.) Example 2 (Modified Laplace’s problem). Let’s assume either person can arrive at any time with probability density function /?(x)=-^exp (|x|15) for -°o<x<o°, having peaks at a distance “d” from each other. A superposition of the two curves (refer to Figure 4) takes the form of the familiar “Golden Gate Bridge” in San Francisco: Arbitrarily setting one peak at x = 0, the required probability density functions become:
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