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?
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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