Question

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?

Answer 1

Answer:

a) 0.964

b) 0.543

Explanation:

Given data:

Total number of card is 140

A) if 20 chips are defective then

we have to find probability that at least one chip in sample is defective

120 chips are non defective

Defective chip denoted by D

hence Probability of at least one chip defective is P(D>1)

as P(D>1) = 1 - P(D=0)

$P(D=0) = \frac{\binom{20}{0}\binom{120}{20}}{\binom{140}{20}}$

P(D)=0.036

so P(D>1) = 1 - P(D=0) = 1-0.036 = 0.964

B) if 5 chips are defective then

we have to find probability that at least one chip in sample is defective

135 chips are non defective

we have to find P(D>1)

so,  P(D>1) =1 - P(D=0)

$P(D=0) = \frac{\binom{5}{0}\binom{135}{20}}{\binom{140}{20}}$

P(D=0) = 0.457

so, $P(D\leq 1) = 1 - 0.457 = 0.543$