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## Homework Statement

A computer program is tested by 5 independent tests. If there is an error, these tests

will discover it with probabilities 0.1, 0.2, 0.3, 0.4, and 0.5, respectively. Suppose that the

program contains an error. What is the probability that it will be found by at least two tests

## Homework Equations

## The Attempt at a Solution

I found the probability that it will happen for at least one:

1-(.9*.8*.7*.6*.5) = .8488

Now my question is: what is the compliment of "at least two tests"

I think for some reason it is "1 and none" but how do I know weather it is "1 and none" or "1 or none"

Pr(at least 2) + Pr(1 and none) = 1

Pr(at least 2) + Pr(1 or none) = 1

it has to be one of these but I'm not sure which.

With Pr(1 and none), Pr(1 and none) = Pr(1)*.8488

With Pr(1 or none) = Pr(1)+Pr(none) - Pr(1)*.8488