A factory received a shipment of 11 hammers, and the vendor who sold the items knows there are 2 hammers in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the hammers in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places

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MrRoyal MrRoyal · Answer 1 · 2021-04-20T06:03:46+02:00

Question:

If a sample of 2 hammer is selected

(a) find the probability that all in the sample are defective.

(b) find the probability that none in the sample are defective.

Answer:

a [tex]Pr = \frac{2}{110}[/tex]

b [tex]Pr = \frac{72}{110}[/tex]

Step-by-step explanation:

Given

[tex]n = 11[/tex] --- hammers

[tex]r = 2[/tex] --- selection

This will be treated as selection without replacement. So, 1 will be subtracted from subsequent probabilities

Solving (a): Probability that both selection are defective.

For two selections, the probability that all are defective is:

[tex]Pr = P(D) * P(D)[/tex]

[tex]Pr = \frac{2}{11} * \frac{2-1}{11-1}[/tex]

[tex]Pr = \frac{2}{11} * \frac{1}{10}[/tex]

[tex]Pr = \frac{2}{110}[/tex]

Solving (b): Probability that none are defective.

The probability that a selection is not defective is:

[tex]P(D') = \frac{9}{11}[/tex]

For two selections, the probability that all are not defective is:

[tex]Pr = P(D') * P(D')[/tex]

[tex]Pr = \frac{9}{11} * \frac{9-1}{11-1}[/tex]

[tex]Pr = \frac{9}{11} * \frac{8}{10}[/tex]

[tex]Pr = \frac{72}{110}[/tex]