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Whether either bus comes soon

EasyProbabilityRandom Variables~3m

Two independent bus lines each have arrival times that are exponential with mean 1010 minutes. Standing at the shared stop, what is the probability that at least one bus arrives within the next 55 minutes? (to 4 decimals)

Show hints (2)+
  1. "At least one" = 1 − P(neither); each line has P(no arrival in 5)=e−5/10P(\text{no arrival in }5) = e^{-5/10}.
  2. Independence: P(neither)=(e−0.5)2=e−1P(\text{neither}) = (e^{-0.5})^2 = e^{-1}.

Answer

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0.6321 (± 0.0005)

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Asked at: Probability & Market-Making, Timed Mental-Math & Sequences

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