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Problem-Solving and Data Analysis / Probability and conditional probability Difficulty: Easy

For a particular machine that produces beads, $29$ out of every $100$ beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?

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Explanation

Choice C is correct. It’s given that $29$ out of every $100$ beads that the machine produces have a defect. It follows that if the machine produces $k$ beads, then the number of beads that have a defect is $StartFraction 29 Over 100 EndFraction k$ , for some constant $k$ . If a bead produced by the machine will be selected at random, the probability of selecting a bead that has a defect is given by the number of beads with a defect, $StartFraction 29 Over 100 EndFraction k$ , divided by the number of beads produced by the machine, $k$ . Therefore, the probability of selecting a bead that has a defect is $StartStartFraction StartFraction 29 Over 100 EndFraction k OverOver k EndEndFraction$ , or $StartFraction 29 Over 100 EndFraction$ .

Choice A is incorrect and may result from conceptual or computational errors.

Choice B is incorrect and may result from conceptual or computational errors.

Choice D is incorrect and may result from conceptual or computational errors.