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Geometric Probability Analysis of Meeting Probability and Intersection Duration for Triple Event Concurrency

Author

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  • Mohammad Al Bataineh

    (Electrical and Communication Engineering Department, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates
    Telecommunications Engineering Department, Yarmouk University, Irbid 21163, Jordan)

  • Zouhair Al-qudah

    (Department of Electrical and Communication Engineering, Al-Hussein bin Talal University, Ma’an 71111, Jordan)

  • Atef Abdrabou

    (Electrical and Communication Engineering Department, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates)

  • Ayman N. Sandokah

    (Al-Faris School, Amman 11732, Jordan)

Abstract

This study investigates the dynamics of three discrete independent events occurring randomly and repeatedly within the interval [ 0 , T ] . Each event spans a predetermined fraction γ of the total interval length T before concluding. Three independent continuous random variables represent the starting times of these events, uniformly distributed over the time interval [ 0 , T ] . By employing a geometric probability approach, we derive a rigorous closed-form expression for the probability of the joint occurrence of these three events, taking into account various values of the fraction γ. Additionally, we determine the expected value of the intersection duration of the three events within the time interval [ 0 , T ] . Furthermore, we provide a comprehensive solution for evaluating the expected number of trials required for the simultaneous occurrence of these events. Numerous numerical examples support the theoretical analysis presented in this paper, further validating our findings.

Suggested Citation

  • Mohammad Al Bataineh & Zouhair Al-qudah & Atef Abdrabou & Ayman N. Sandokah, 2023. "Geometric Probability Analysis of Meeting Probability and Intersection Duration for Triple Event Concurrency," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2708-:d:1171599
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