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printed circuit cards are placed in a functional test after being populated with semiconductor chips. a lot contains 190 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? round your answers to four decimal places (e.g. 0.9876). (a) the probability is enter your answer in accordance to the item a) of the question statement (b) the probability is

Answer :

(a) if 20 cards are defective, then the probability that at least 1 defective card is in the sample is 0.964​

(b) if 5 cards are defective, then the probability that at least 1 defective card appears in the sample is 0.543​

Probability:

In statistics, probability refers the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

Given,

Here we have a printed circuit cards are placed in a functional test after being populated with semiconductor chips. a lot contains 190 cards, and 20 are selected without replacement for functional testing.

And we need to find the following probability.

Here we have to recall the formula for probability mass function of the hypergeometric random variable X with the parameters

N = 190

n ​= 20​

and the parameter K.

And it is the following expression:

f(x) = [(K x) (140 - k 20 - x)] / (140 20)

Now, we have to Set K=20 and calculate from the probability mass function:

=> P(X≥1)=1−f(0)=0.964​

And then Set K=5 and calculate from the probability mass function:

=> P(X≥1)=1−f(0)=0.543​

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