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There would be a 90.25% of the event happening in neither trial(.95*.95), a 0.25% chance of the event happening in both trials(.05*.05), a 4.75% of it happening in trial A but not B(.95*.05) and a 4.75% chance of it happening in trial B but not A(.05*.95).
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The probability of the event NOT happening in either trial is (1-.05) *(1-.05) = .9025.
The probability of the event happening in at least one of the two trials is 1-.9025 = .0975.