A typical box of 100 transistors contains 2 defective items. It is realized among the last 10 boxes, one box has 10 defective transistors. An inspector picks one of these 10 boxes at random and the first transistor is not defective. What’s the probability this box is the bad one?

A typical box of 100 transistors contains 2 defective items. It is realized among the last 10 boxes, one box has 10 defective transistors. An inspector picks one of these 10 boxes at random and the first transistor is not defective. What’s the probability this box is the bad one?

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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Expert Solution

Step 1: Given

Number of transistors a box contains=100

out of which 2 are defective items.

Among the last 10 boxes, one box has 10 defective items.

P( 10 defective transitiors box) = 1/10 = 0.1
P( 1 defective transistor) = 9/10 = 0.9

AND,

P( first tested is defective | 10 defective transitiors box) = 10/100 = 0.1
P( first tested is defective | 1 defective transitiors box) = 1/100 = 0.01

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