You still have those two boxes. But now, more generally, units manufactured by A are defective with probability pa, while units manufactured by B are defective with probability pb. You select a box at random and test N units from it. Express: a) The probability that exactly k of the tested units are defective. b) Given that k of the tested units are defective, the probability that the box you are testing contains the units manufactured by A.

You still have those two boxes. But now, more generally, units manufactured by A are defective with probability pa, while units manufactured by B are defective with probability pb. You select a box at random and test N units from it. Express: a) The probability that exactly k of the tested units are defective. b) Given that k of the tested units are defective, the probability that the box you are testing contains the units manufactured by A.

A First Course in Probability (10th Edition)

10th Edition

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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Question

Yet another variation on Problem # 1: You still have those two boxes. But now, more generally, units manufactured by A are defective with probability pa, while units manufactured by B are defective with probability pb. You select a box at random and test N units from it. Express:

a) The probability that exactly k of the tested units are defective.

b) Given that k of the tested units are defective, the probability that the box you are testing contains the units manufactured by A.

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