# Somthing went wrong, A sample of 5 is selected from 40 (image included)

• mr_coffee
In summary, the conversation discusses a problem involving selecting a sample of 5 computer boards from a production run of 40, where 3 boards are already known to be defective. The problem asks how many samples will contain at least one defective board and the probability of choosing a sample with at least one defective board. The solution involves using the set difference rule and correctly computing the number of samples with no defects to arrive at the correct answers for both parts.
mr_coffee
Hello everyone. I think I have part a of this problem right but part b must be wrong becuase when I did the probabily it was like 99.994% chance that at least 1 board would be defective.

Heres the problem:
Suppose that three computer boards in a production run of forty are defective. A Sample of 5 is to be selected to be checked for defects.

Part a also might be wrong though, becuase I used 40 possible boards might be defective...but in the beginning they said 3 out of the 40 already where found to be defective, so would I use 38 instead of 40?

a. How many different samples can be chosen?
b. How many samples will contain at least one defective board?
c. What is the probability that a randomly chosen sample of 5 contains at least one defective board?

Heres my work for a, b, and c.

For part, b, i used 40-3, because at the beginning of the problem they said 3 out of the 40 boards were defective. So i thought, well you know 38 of the boards may or may not be defective, but u already used 3 out of the 40, so you only have 38 to choose from now.

http://suprfile.com/src/1/40tbojq/lastscan.jpg

Hm..it seems they disabled embeded images? Just click the link to dispaly the image.

Thanks!

PS: I used the difference rule. I was modeling my problem after another problem the book did.
There problem was the following:

Suppose the group of 12 consist of 5 men and 7 women.
b. How many 5 person teams contain at least one man?

There solution to this was:
Observe that the set of 5 person teams containing at least one man equals the set difference between the set of all 5 person teams and the set of 5 person teams that do not contain any men.

now a team with no men consist entirely of 5 women chosen from the seven women in the group, so there are 7 choose 5 such teams. The total number of 5 person teams is 12 choose 5 = 792, so:

[# of teams with at least 1 man] = [total number of teams of 5] - [# of teams of 5 that do not contain any men]
= (12 choose 5) - (7 choose 5) = 792 - 7!/(5!2!)
= 792 -12 = 771.

Last edited by a moderator:
I think you are right, 99% seems way too high. Your part (a) is fine. You have the right idea for part (b) but you computed the number of samples that have no defects incorrectly. You said there are 40-3 = 37 good boards. So how many samples are there from these good boards? Once you have that you should get the right answer for (b) and then use your same idea for (c) and you should get the probability to be ~ .337

Aw3some thanks matt!

37 choose 5 = 435897
222111/658008 = .3376 = 33.76% that sounds more like it!

## 1. What is the probability of getting a perfect sample of 5 from a population of 40?

The probability of getting a perfect sample of 5 from a population of 40 is extremely low. It would be 1 in 658,008, or approximately 0.0000015%

## 2. How can we ensure that the sample of 5 is representative of the entire population?

To ensure that the sample of 5 is representative of the entire population, we can use random sampling techniques such as simple random sampling, stratified sampling, or cluster sampling. These methods help to reduce bias and ensure that every member of the population has an equal chance of being selected for the sample.

## 3. Can we make any generalizations about the entire population based on a sample of 5?

No, it is not appropriate to make generalizations about the entire population based on a sample of 5. The sample size is too small to accurately represent the entire population and can lead to biased or incorrect conclusions.

## 4. How does the sample size affect the accuracy of the results?

The sample size has a direct effect on the accuracy of the results. Generally, a larger sample size will lead to more accurate results as it reduces the margin of error and increases the representativeness of the sample.

## 5. What are the potential sources of error in this sampling situation?

There are several potential sources of error in this sampling situation, such as sampling bias, selection bias, and measurement error. Additionally, the random selection process may also lead to a less representative sample if the sample size is small.

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