# Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 6 of which have electrical defects and 19 of which have mechanical defects. a. How many ways are there to randomly select 5 of these key boards for a thorough inspection (without regard to order)? b. In how many ways can a sample of 5 keyboards be selected so that exactly two have an electrical defect? c. If a sample of 5 keyboards is randomly selected, what is the probability that at least 4 of these will have a mechanical defect?

### Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

### Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

#### Solutions

Chapter
Section
Chapter 2.3, Problem 34E
Textbook Problem

## Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 6 of which have electrical defects and 19 of which have mechanical defects. a. How many ways are there to randomly select 5 of these key boards for a thorough inspection (without regard to order)? b. In how many ways can a sample of 5 keyboards be selected so that exactly two have an electrical defect? c. If a sample of 5 keyboards is randomly selected, what is the probability that at least 4 of these will have a mechanical defect?

Expert Solution

a.

To determine

Find the number of ways to select 5 keyboards for thorough inspection.

### Explanation of Solution

Given info:

There are 25 keyboard failures out of which 6 has electrical defects and 19 has mechanical defects.

Calculation:

Combination:

A combination is a selection of objects without regard to order. It may denoted as Ck,n

The expression for the combination is,

Ck,n=n!k!(nk)!

Here, n represents the group size and k represents the subset size.

Here, order does not matter. Hence, combination is used

Expert Solution

b.

To determine

Find the number of ways to select 5 keyboards that has exactly 2 electrical defects.

Expert Solution

c.

To determine

Find the probability that 4 keyboards have mechanical defects.

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