Question

A factory received a shipment of 37 sprockets, and the vendor who sold the items knows there are 4 sprockets in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the sprockets in the sample are defective, he will refuse the shipment.For each of the following, give your responses as reduced fractions.If a sample of 4 sprockets is selected, find the probability that all in the sample are defective. If a sample of 4 sprockets is selected, find the probability that none in the sample are defective.

Answer 1

Given:

Required:

The probability that all in the sample are defective.

The probability that none in the sample is defective.

Step-by-step explanation:

(a) 5 sprockets are selected probability that all are defective favorable cases are 1 which means all 4 are defective.

The number of ways of selecting 4 from 4 defective sprockets is,

`^4C_4`

The required probability is calculated as,

`\begin{gathered} Probability=\text{ }(^4C_4)/(^(37)C_4) \\ Probability=\text{ }(1)/(66045) \\ \end{gathered}`

Thus the probability that all selected is 1/66045.

(b) The 4 sprockets selected are non-defective.

The number of ways of selecting 4 sprockets is,

`^(33)C_4`
`^4C_4`

The required probability is calculated as,

`\begin{gathered} Probability\text{ = }(^(33)C_4)/(^(37)C_4) \\ Probability\text{ = }(40920)/(66045) \\ Probability\text{ = 0.6196} \end{gathered}`

Answer:

Thus the probability that all selected is 1/66045.

Thus the probability of selecting 4 non-defective sprockets is 0.6196.