Find the probability of a defective item in a small sample

[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

Homework Equations

The Attempt at a Solution

I think I know the answer but I need explanation.

 

[awkward]

If you think you know the answer, how about sharing your solution with us?

 

[lorik]

If you think you know the answer, how about sharing your solution with us?

permutation


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

But still need explenation though.

 

[awkward]

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?

 

[lorik]

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 ?

 

[awkward]

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).