A certain electronic component is produced by two manufacturers A and B. Units from A are more expensive and the probability of a defective unit is 1/4. Units from B are cheap but defective with (appalling) probability 1/2. You stocked up on units from both sources, and stored them in two separate boxes according to manufacturer. But the boxes are, unfortunately, no longer labeled. You select a box at random and pick a unit. If it turns out to be defective, you guess that it was manufactured by B (reasoning that this is the more likely explanation of the observation), and similarly, if it works you guess that the unit was manufactured by A. Find the probability that your guess is wrong.

A certain electronic component is produced by two manufacturers A and B. Units from A are more expensive and the probability of a defective unit is 1/4. Units from B are cheap but defective with (appalling) probability 1/2. You stocked up on units from both sources, and stored them in two separate boxes according to manufacturer. But the boxes are, unfortunately, no longer labeled. You select a box at random and pick a unit. If it turns out to be defective, you guess that it was manufactured by B (reasoning that this is the more likely explanation of the observation), and similarly, if it works you guess that the unit was manufactured by A. Find the probability that your guess is wrong.

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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