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# A lot of 1000 components contains 300 that are defective. ISBN: 9780073401331 38

## Solution for problem 24E Chapter 2.3

Statistics for Engineers and Scientists | 4th Edition

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Problem 24E

A lot of 1000 components contains 300 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.

a. Find P(A).

b. Find P(B|A) .

c. Find P(A ∩ B).

d. Find P(Ac ∩ B).

e. Find P(B) .

f. Find P(A|B).

g. Are Aand B independent? Is it reasonable to treat A and B as though they were independent? Explain.

Step-by-Step Solution:

Step 1 of 8 :

Given,  300 are defective in a lot of 1000 components. Two components are drawn at random and tested.

Let A be the event that the first component drawn is defective and B be the event that the second component drawn is defective.

Step 2 of 8 :

The claim is to find the the probability of first component is defective

That is P(A)

Where, A is the event that the first component drawn is defective.

We have 1000 components, in that 300 are defectives.

then, P(first component is defective) = = = Therefore, P(A) = 3/10.

Step 3 of 8 :

b)

the claim is to find the P(B/A)

If A occurs, then there are 999 components remaining.

In remaining 999 components 299 are defectives

Then, P(B/A) = = .

Therefore, P(B/A) = .

Step 4 of 8 :

c)

The claim is to find P( )

We know that

P( )  = P(A) P(B/A)

= ( ) ( )

= Therefore, P( )  = .

Step 5 of 8

Step 6 of 8

##### ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: Find, drawn, defective, let, components. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 24E from 2.3 chapter was answered, more than 2404 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 24E from chapter: 2.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “A lot of 1000 components contains 300 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.a. Find P(A).________________b. Find P(B|A) .________________c. Find P(A ? B).________________d. Find P(Ac ? B).________________e. Find P(B) .________________f. Find P(A|B).________________g. Are Aand B independent? Is it reasonable to treat A and B as though they were independent? Explain.” is broken down into a number of easy to follow steps, and 79 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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