# Find the probability of a defective item in a small sample

• lorik
In summary: Close but not quite right. The complication is that the draws are not independent events. Since you are drawing balls without replacement, if you draw a good ball on the first draw it changes the probability that you will draw a bad draw on the second draw. Numerically, there won't be much difference, in this case, though-- you could say the draws are "almost independent".
lorik

## Homework Statement

In a box there are 25 non defective details and 28 defective details find propability from two random extraction that
c) One of them is non-defective

## The Attempt at a Solution

I think I know the answer but I need explanation.

awkward said:
permutation

C25(1) * C28(1)/ C53(2) = 700/(2756/2) =1400/2756

But still need explenation though.

You have the right idea but you need to check your numbers.

There are C(53,2) ways to draw 2 items from the box. We assume all of these are equally likely. Of these, how many consist of one defective and one non-defective?

awkward said:
You have the right idea but you need to check your numbers.

There are C(53,2) ways to draw 2 items from the box. We assume all of these are equally likely. Of these, how many consist of one defective and one non-defective?

It should be about 50% chance of one consisting non defective and the other being defective I THINK

in practice assume we have 50 balls 25 good and 25 bad ,we draw 2 balls and it should be G1/2 * B1/2 ?

lorik said:
It should be about 50% chance of one consisting non defective and the other being defective I THINK

in practice assume we have 50 balls 25 good and 25 bad ,we draw 2 balls and it should be G1/2 * B1/2 ?
Close but not quite right. The complication is that the draws are not independent events. Since you are drawing balls without replacement, if you draw a good ball on the first draw it changes the probability that you will draw a bad draw on the second draw. Numerically, there won't be much difference, in this case, though-- you could say the draws are "almost independent".

One way to approach this type of problems is the way I outlined previously. All C(50,2) combinations of 50 balls taken two at a time are equally likely. So count the number of ways to draw one good and one bad, then divide by C(50,2).

## What is the definition of probability?

Probability is the measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

## How is probability calculated?

To calculate the probability of an event, divide the number of favorable outcomes by the total number of possible outcomes. This is known as the classical definition of probability.

## What is a small sample?

A small sample refers to a subset of a larger population. It is typically used in statistical analysis when it is not feasible or practical to collect data from the entire population.

## How does sample size affect the probability of a defective item?

The larger the sample size, the more accurate the estimation of the probability of a defective item. This is because a larger sample size reduces the effect of random chance and provides a more representative sample of the population.

## What are some factors that can affect the probability of a defective item in a small sample?

Some factors that can affect the probability of a defective item in a small sample include the quality control measures in place, the production process, and the characteristics of the item itself. Additionally, sampling methods and sample size can also impact the probability.

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