What is the Probability of Selecting 9 CDs with Saved Data from a Box of 15 CDs?

[NewtonianAlch]

There are 15 CDs in a box. On 10 of the CDs there are saved data files,
and the other CDs have no data files saved on them.

i) Suppose that 12 CDs are randomly selected. Determine the probability that exactly 9 of these CDs selected have saved data files.

I'm not sure how to do this. First I thought some kind of conditional probability? But I'm confused about that.

P(A|B) = P(A intersection B)/P(B)?

Is that simply [P(A)*P(B)]/P(B) ? Wouldn't the P(B)'s cancel out?

If not, then if 12 are selected. The probability of any of them having data is (10/15)*(12/15) = 8/15

Now,

(9/12)*(8/15) = 40% [probability of 9 of those having any data from the 12 selected]

 

[haruspex]

P(A|B) = P(A intersection B)/P(B)?

Is that simply [P(A)*P(B)]/P(B) ? Wouldn't the P(B)'s cancel out?

No, P(A intersection B) is the probability of A and B occurring together. It only reduces to P(A)*P(B) if they're independent. In another extreme, A might imply B, in which case it reduces to P(A).
How many equally likely ways are there of picking 12 of the 15? In how many of these do you get exactly 9 with data?

 

[lyuriedin]

As long as the CDs aren't being placed back in the box after each selection, it should be a binomial distribution.

 

[NewtonianAlch]

No, P(A intersection B) is the probability of A and B occurring together. It only reduces to P(A)*P(B) if they're independent. In another extreme, A might imply B, in which case it reduces to P(A).
How many equally likely ways are there of picking 12 of the 15? In how many of these do you get exactly 9 with data?

Hmm...15C12 = 455?

Then 9/455?

 

[haruspex]

Hmm...15C12 = 455?

Then 9/455?

455 is right but 9 is wrong. Need to pick 9 of the ten and one of the 5.

 

[NewtonianAlch]

I don't quite follow, do you mean 15C12 * (9/10)*(1/5) ?

 

[haruspex]

I don't quite follow, do you mean 15C12 * (9/10)*(1/5) ?

No. Want
number of ways of choosing 9 from the 10 and 1 from the 5
Since these are independent, that's
(number of ways of choosing 9 from the 10) * (number of ways of choosing 1 from the 5)
right?

 

[Norwegian]

455 is right but 9 is wrong. Need to pick 9 of the ten and one of the 5.

9 is right, but "one" is wrong. You need to pick 3 of the 5 blank CDs.

(edit: btw, the problem is somewhat easier to grasp, if you replace it with drawing 3 CDs, and ask about the probability of exactly one having data)

 

[NewtonianAlch]

Now I'm super confused.

What exactly is happening here? Is this some kind of binomial distribution like someone posted earlier.

 

[haruspex]

9 is right, but "one" is wrong. You need to pick 3 of the 5 blank CDs.

Sorry - got confused between the number of CDs with data and the number to be chosen.
So it's:
number of ways of choosing 9 from the 10 and 3 from the 5
Since these are independent, that's
(number of ways of choosing 9 from the 10) * (number of ways of choosing 3 from the 5)