   Chapter 9.9, Problem 29ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Suppose that ten items are chosen at random from a large batch delivered to a company. The manufacturer claims that just 3% of the items in the batch are defective. Assume that the batch is large enough so that even thought the selection is made without replacement, the number 0.03 can be used to appropriate the probability that any one of the ten items is defective. In addition, assume that because the items are chosen at random, the outcomes of the choices are mutually independent. Finally, assume that the manufacturer’s claim is correct. What is the probability that none of the ten is defective? What is the probability that at least one of the ten is defective? What is the probability that exactly four of the ten are defective? What is the probability that at most two of the ten are defective?

To determine

(a)

To find out the probability that none of the ten is defective.

Explanation

Given information:

The manufacturer claims that just 3% of the items are defective. Total ten items are chosen from a large batch.

Calculation:

According to the given information the following things can be written

P(defective item)=0.03P(non defective item)=0

To determine

(b)

To find out the probability that at least one of the ten is defective.

To determine

(c)

To find out the probability that exactly four of the ten is defective.

To determine

(d)

To find out the probability that at most two of the ten is defective.

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