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## Homework Statement

Generalize to obtain (C

_{1}U C

_{2}U...U C

_{k})' = C

_{1}' intersect C

_{2}' intersect...intersect C

_{k}'

' = complement

Say that C

_{1}, C

_{2},...,C

_{k}are independent events that have respective probabilities p

_{1}, p

_{2}, ..., p

_{k}. Argue that the probability of at least one of C

_{1}, C

_{2},...,C

_{k}is equal to 1 - (1-p

_{1})(1-p

_{2})...(1-p

_{k})

## Homework Equations

I don't know how to generalize that...

For the second part, P(C

_{1}U C

_{2}U...U C

_{k}) = 1- P(C

_{1}U C

_{2}U...U C

_{k})' = 1 - P(C

_{1}' intersect C

_{2}' intersect...intersect C

_{k}') = 1 - (1-p

_{1})(1-p

_{2})...(1-p

_{k}). Not sure how that proves at least one of C

_{k}has to equal that though...