A shipment of 10 items has two defective and eight nondefective items. In the inspection of the shipment, a sample of items will be selected and tested. If a defective item is found, the shipment of 10 items will be rejected. (a) If a sample of three items is selected, what is the probability that the shipment will be rejected? (b) If a sample of four items is selected, what is the probability that the shipment will be rejected? (c) If a sample of five items is selected, what is the probability that the shipment will be rejected? ke a 0.90 probability of rejecting a shipment with two defective and eight nondefective items, how large a sample would you recom- mend?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A shipment of 10 items has two defective and eight nondefective items. In the inspection of the shipment, a sample of items will be selected and tested. If a defective item is found, the shipment of 10 items will be rejected. (a) If a sample of three items is selected, what is the probability that the shipment will be rejected? (b) If a sample of four items is selected, what is the probability that the shipment will be rejected? (c) If a sample of five items is selected, what is the probability that the shipment will be rejected? ke a 0.90 probability of rejecting a shipment with two defective and eight nondefective items, how large a sample would you recom- mend?
3. There are n children in a given kindergarten. When leaving the kindergarten each
child chooses at random one left and one right shoe. Prove that:
(a) The probability Pa that none of the children will bring home his or her own
pair of shoes is given by
Pa =E(-1)*
(n – k)!
k!n!
k=1
(b) The probability P, that none of the children will bring home at least one of his
or her own shoes is given by
2
P, = (E(-1)*.
k=2
Hint. First, one must give meaning to the phrase "each of the n children
chooses at random one left and one right shoe"
Transcribed Image Text:3. There are n children in a given kindergarten. When leaving the kindergarten each child chooses at random one left and one right shoe. Prove that: (a) The probability Pa that none of the children will bring home his or her own pair of shoes is given by Pa =E(-1)* (n – k)! k!n! k=1 (b) The probability P, that none of the children will bring home at least one of his or her own shoes is given by 2 P, = (E(-1)*. k=2 Hint. First, one must give meaning to the phrase "each of the n children chooses at random one left and one right shoe"
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