Problem 146E

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?

Solution :

Step 1 of 2:

Given lot contains 140 cards.

So N=140.

Then 20 are selected without replacement, n=20.

Let X follows Hypergeometric with parameters N, n, and k.

The probability mass function is

f(x)= P(X=x)

P(X=x) =

Where,

N = population size =800 and

n = sample size = 10.

Our goal is:

a). We need to find the probability that at least one defective card is in the sample.

b). We need to find the probability that at least one defective card appears is in the sample.

a). Given 20 cards are defective.

So K=20.

Then the probability that at least one defective card is

P(X1) = 1-P(X=0)

P(X1) = 1-

P(X1) = 1-

P(X1) = 1-

P(X1) = 1-0.03561

P(X1) = 0.9643

Therefore, the probability that at least one defective card is 0.9643.