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Miscellaneous Topics

In: Elementary Probability Theory

Author

Listed:
  • Melvin Hausner

    (New York University, Washington Square and University College)

Abstract

Suppose that an experiment has probability space S, and that A is an event of S with probability p = p(A). We let P n denote the probability that the event A will occur at least once if the experiment is repeated, independently, for n times. By Theorem 37 of Chapter 3, we have 4.1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa % aaleaacaWGUbaabeaakiabg2da9iaaigdacqGHsislcaGGOaGaaGym % aiabgkHiTiaadchacaGGPaWaaWbaaSqabeaacaWGUbaaaaaa!3FB6! $$ {P_n} = 1 - {(1 - p)^n} $$ The cases p = 0 and p = 1 naturally give P n = 0 and P n = 1, while the case n = 1 naturally gives P 1 = p. We shall therefore usually assume that n > 1 and 4.2 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGimaiabgY % da8iaadchacqGH8aapcaaIXaaaaa!3A66! $$ 0

Suggested Citation

  • Melvin Hausner, 1995. "Miscellaneous Topics," Springer Books, in: Elementary Probability Theory, chapter 0, pages 123-151, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-1753-5_4
    DOI: 10.1007/978-1-4615-1753-5_4
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