Probability of Defective Photocopiers

[anon2020]

There are seven photocopiers, and three of these photocopiers are defective. The buyer begins to test them one at a time to figure out which three are defective.

a) Given that exactly two of the defective photocopiers were found within the tests 1, 3, 5, what is the probability the other defective photocopier was found on tests 6 or 7?
b) Given the last defective photocopier was found within the last two tests, what is the probability that the first two defective photocopiers were found within the first three tests?

I'm not sure how to set up these answers. I've tried a few different ways and get stuck every time. Any help in the right direction would be greatly appreciated!

 

[Deleted member 4993]

There are seven photocopiers, and three of these photocopiers are defective. The buyer begins to test them one at a time to figure out which three are defective.

a) Given that exactly two of the defective photocopiers were found within the tests 1, 3, 5, what is the probability the other defective photocopier was found on tests 6 or 7?
b) Given the last defective photocopier was found within the last two tests, what is the probability that the first two defective photocopiers were found within the first three tests?

I'm not sure how to set up these answers. I've tried a few different ways and get stuck every time. Any help in the right direction would be greatly appreciated!

Please share at least one of those "ways" with us.

That will give us some idea about where to begin to help you.

 

[anon2020]

Please share at least one of those "ways" with us.

That will give us some idea about where to begin to help you.

So for part a, my initial thought was to do P(one defective on test 6 or 7|two defective within tests 1,3,5)=P(two defective within tests 1,3,5 and one defective on test 6 or 7)/P(two defective within tests 1,3,5) but I'm not sure how to go about finding the probability of two defective within tests 1,3,5. Am i supposed to find the sum of each test or is there a more specific way to solve for that?

I think I've managed to work out part b so part a is really the one that I'm stuck on. I think I'm most confused by the idea of the tests being 1,3, and 5 instead of 1-5.

 

[Steven G]

There are seven photocopiers, and three of these photocopiers are defective. The buyer begins to test them one at a time to figure out which three are defective.

a) Given that exactly two of the defective photocopiers were found within the tests 1, 3, 5, what is the probability the other defective photocopier was found on tests 6 or 7?
b) Given the last defective photocopier was found within the last two tests, what is the probability that the first two defective photocopiers were found within the first three tests?

I'm not sure how to set up these answers. I've tried a few different ways and get stuck every time. Any help in the right direction would be greatly appreciated!

You really should show your work. Problems like this are done with different styles of thinking. If you show us how you are thinking about it someone here are help you figure this out the way you want.

Haven't said that I will give you some hints.
For part a the problem reduces to knowing that there is one defective copier in 2,4,6 and and you want to findi the probability the defective copier is 6 or 7.
Part b reduces to: One defective copier is 6 or 7 (not both). Find the probability that the other two defective copiers are amongst 1,2 and 3

 

[Steven G]

So for part a, my initial thought was to do P(one defective on test 6 or 7|two defective within tests 1,3,5)=P(two defective within tests 1,3,5 and one defective on test 6 or 7)/P(two defective within tests 1,3,5) but I'm not sure how to go about finding the probability of two defective within tests 1,3,5. Am i supposed to find the sum of each test or is there a more specific way to solve for that?

I think I've managed to work out part b so part a is really the one that I'm stuck on. I think I'm most confused by the idea of the tests being 1,3, and 5 instead of 1-5.

Yes, one needs to know what test means! I am thinking that the copiers are numbered 1-7 and by test 1, 3 5 it means that copier numbered 1, 3 and 5 were tested.

What answer did you get for part b? You found an answer even though you did not know what test means????
Can you post a picture of the entire problem?

 

[Agent Smith]

Would like some help with solving this problem.

Answer to question a) Since there are 3 defective machines and the first 2 were already detected by the 5th test, the probability that the last will be detected on tests 6 OR 7 is 1.

Answer to question b) is [imath]\frac{ _3C_2}{2^3}[/imath]