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StatisticsProbability and Statistics for Engineering and the SciencesComputer 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?BuyFind*arrow_forward*

9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

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.

**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

The expression for the combination is,

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.

Probability and Statistics for Engineering and the Sciences

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