Let {N_1(t)} and {N_2(t)} be two independent  Poisson processes with rates λ1=1 and λ2=2, respectively.  Find the probability that the second arrival in N_1(t) occurs before the third arrival in N_2(t). Round answer to 4 decimals.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Let {N_1(t)} and {N_2(t)} be two independent  Poisson processes with rates λ1=1 and λ2=2, respectively.  Find the probability that the second arrival in N_1(t) occurs before the third arrival in N_2(t). Round answer to 4 decimals.

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