Question

Abatchof140semiconductorchipsisinspected by choosing a sample of 5 chips without replacement. Assume 10 of the chips do not conform to customer requirements.
a. How many different samples are possible?
b. How many samples contain exactly one nonconforming chip?
c. How many samples contain at least one nonconforming chip?]

Answer 1

Answer:

Step-by-step explanation:

given that a batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips without replacement.

10 chips do not conform to customer requirements.

i.e. out of 140 chips 10 are defective and 130 are good

a) 5 chips can be selected form 140 chips in 140C5 ways

= 416965528

b) For containing exactly one non conforming chip we have one selected from 10 and other 4 selected from 130

No of ways = $10C1 (130C4)\\=10(11358880)\\=113588800$

c) For atleast one nonconforming chip we can calculate as total - no non conforming

i.e. $416965528-130C5\\= 416965528-286243776\\=130721752$