1.Before being allowed to enter a maximum-security area at a military installati

Question

1.Before being allowed to enter a maximum-security area at a military installation, a person must pass three independent identification tests: a voice-pattern test, a fingerprint test, and a handwriting test. If the reliability of the first test is 98%, that of the second test is 98.2%, and that of the third is 98.2%, what is the probability that this security system will allow an improperly identified person to enter the maximum-security area? (Round your answer to seven decimal places.)
2.Copykwik has four photocopy machines: A, B, C, and D. The probability that a given machine will break down on a particular day is given below.

P(A) =

    P(B) =

    P(C) =

    P(D) =

Assuming independence, what is the probability on a particular day that the following will occur?

(a) All four machines will break down (Round your answer to ten decimal places.)


(b) None of the machines will break down (Round your answer to three decimal places.)

Explanation / Answer

1. P(System allows an improperly identified person to the maximum security area)

= P(All the three system failed)

= P(1st wrong) * P(2nd wrong) * P(3rd wrong)

= (1 - 0.98) * (1 - 0.982) * (1 - 0.982)

= 0.0000065

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