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Let A1, A2, . . . , An be n independent events in a sample space...

Let A1, A2, . . . , An be n independent events in a sample space Ω, with respective probability pi = P (Ai). Give a simple expression for the probability P(A1 ∪A2 ∪...∪An) in terms of p1, p2, ..., pn. Let us now apply your result in a practical setting: a robot undergoes n independent tests, which are such that for each test the probability of failure is p. What is the probability that the robot fails at least one of the tests?

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Answer #1

P( A1 U A2 U....... U An ) = p1 + p2 + p3 + ..... + pn

and

Probability that the robot fails atleast one of the tests =( 1 - ( 1 - p )n )

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