Suppose a lot contains 100,000 items. The proportion of defectives p in a good lot is 0.2 with probability 0.8, and 0.4 in a bad lot with probability 0.2. Accepting a bad lot costs $300 and rejecting a good lot costs $200. Sampling costs 1$ per item. Suppose that sampling continues until we observe the kth defective item, at which it stops. Find the optimal value of k.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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Suppose a lot contains 100,000 items. The
proportion of defectives p in a good lot is 0.2
with probability 0.8, and 0.4 in a bad lot with
probability 0.2. Accepting a bad lot costs $300
and rejecting a good lot costs $200. Sampling
costs 1$ per item. Suppose that sampling
continues until we observe the kth defective
item, at which it stops. Find the optimal value
of k.
Transcribed Image Text:Suppose a lot contains 100,000 items. The proportion of defectives p in a good lot is 0.2 with probability 0.8, and 0.4 in a bad lot with probability 0.2. Accepting a bad lot costs $300 and rejecting a good lot costs $200. Sampling costs 1$ per item. Suppose that sampling continues until we observe the kth defective item, at which it stops. Find the optimal value of k.
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