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2 October, 12:36

Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 110 cards, and 20 are selected without replacement for functional testing.

(a) If 20 cards are defective, what is the probability that at least 1 defective card is in the sample?

(b) If 5 cards are defective, what is the probability that at least 1 defective card appears in the sample?

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  1. 2 October, 16:23
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    The answers to the questions are;

    (a) P (At least 1 defective)

    = 0.9883.

    (b) P (At least 1 defective)

    = 0.6409.

    Step-by-step explanation:

    There are 110 cards and 20 defectives.

    a) The probability of at least one defective is given by

    P (At least 1 defective) = 1 - P (0 defective)

    P (0 defective) = 20C0 * (90C0) / (110C20) = 0.0116

    1 - 0.0116 = 0.9883

    b) For a set of 110 boards that has 5 defective and 105 non-defective

    P (At least 1 defective) = 1 - P (0 defective)

    P (0 defective) = (20C0) (90C5) / (110C5) = 0.35909

    1-0.35909

    = 0.6409
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