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24 April, 06:01

Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 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. 24 April, 06:15
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    a) 0.9644 or 96.44%

    b) 0.5429 or 54.29%

    Step-by-step explanation:

    a) The probability that at least 1 defective card is in the sample P (A) = 1 - probability that no defective card is in the sample P (N)

    P (A) = 1 - P (N) ... 1

    Given;

    Total number of cards = 140

    Number selected = 20

    Total number of defective cards = 20

    Total number of non defective cards = 140-20 = 120

    P (N) = Number of possible selections of 20 non defective cards : Number of possible selections of 20 cards from all the cards.

    P (N) = 120C20/140C20 = 0.0356

    From equation 1

    P (A) = 1 - 0.0356

    P (A) = 0.9644 or 96.44%

    b) Using the same method as a) above

    P (A) = 1 - P (N) ... 1

    Given;

    Total number of cards = 140

    Number selected = 20

    Total number of defective cards = 5

    Total number of non defective cards = 140-5 = 135

    P (N) = 135C20/140C20 = 0.457

    From equation 1

    P (A) = 1 - 0.4571

    P (A) = 0.5429 or 54.29%
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