Two searches, neither hits

You run two independent search processes in parallel. Each process, on each of its trials, succeeds with probability 0.250.25. What is the probability that after 2 trials neither process has produced a single success? Give a decimal to four places.

Show hints (2)+
  1. One process has no success in 2 trials with probability 0.7520.75^2.
  2. Two independent processes: multiply, giving 0.7540.75^4.

Answer

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0.3164 (± 0.001)

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