Question

A factory received a shipment of 17 compressors, and the vendor who sold the items knows there are 8 compressors in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the compressors in the sample are defective, he will refuse the shipment.7. For each of the following, give your responses as reduced fractions.If a sample of 8 compressors is selected, find the probability that all in the sample are defective. If a sample of 8 compressors is selected, find the probability that none in the sample are defective.

Answer 1

Given

Total compressors = 17

Defective = 8

Find

a) If a sample of 8 compressors is selected, probability that all 8 are defective.

b) If a sample of 8 compressors is selected, probability that none in the sample are defective.

Explanation

a)

there are 8 defective compressors in the shipment of 17

therefore , the probability that all the samples are defective =

$\frac{^8C_8}{^{17}C_8}=\frac{1}{\frac{17!}{8!9!}}=\frac{1}{24310}$

b)

there are 9 non defective compressors in the shipment of 17.

therefore , the probability that none in the samples are defective =

$\frac{^9C_8}{^{17}C_8}=\frac{9}{24310}$

Final Answer

Therefore ,

a) probability that all 8 are defective = 1/24310

b) probability that none in the sample are defective = 9/24310