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Finding the probability of observing an event.

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Items coming off a production line are categorized as good (G), slightly blemished (B), and defective (D), and the percentages are 80%, 15% and 5%, respectively. Suppose that two items will be randomly selected for inspection and the selections are independent.
(a) List all outcomes and assign probabilities.
(b) Find the probability that at least one of the items is slightly blemished.
(c) Find the probability that neither of the items is good.

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Solution Summary

This problem begins by calculating all the probabilities associated with selecting two items from an assembly line as a sample. Next the probabilities of of finding products in various conditions in the sample, namely: blemished or good. Responses are hand calculated.

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Solution. We label two items, i.e., item 1 and item 2. If two items are good, we denote it by GG; similarly GB denotes that item 1 is good and item 2 is slightly blemished; and so on.
(a)There are 9 possible ...

Solution provided by:
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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