Christmas Probability Problem

A box contains two defective Christmas tree lights that have been inadvertently mixed with eight nondefective lights. If the lights are selected one at a time without replacement and tested until both defective lights are found, what is the probability that both defective lights will be found within three trials? (Round your answer to four decimal places.)

Okay it helps if I see things...haha (so 0 is for good light, x is for bad light)
0 0 0 0 x
0 0 0 0 x

So if you try three times... well this is what I tried and its not right. (3/10) (2/9) (1/8).... ideas??

This is a hypergeometric probability.

If there are N elements of which M are successes and N-M are failures, the probability of getting x successes in n trials is given by


\(\displaystyle \frac{\binom{M}{x}\binom{N-M}{n-x}}{\binom{N}{n}}\)

In this case, you could think of the defective bulbs has the successes.

So what's the probability? What do I substitute for each letter??

It's all given to you in the problem. Fill in the formula.

So this is what I put in and it didn't work...

( (2 C 2) (8-2 C 3-2) )/ (8 C 3)

The problem states 'within' 3 trials. So, it is poossible to get them both in two trials as well.

This doesn't make sense. Can you explain it more?

bubbagump said:

This doesn't make sense. Can you explain it more?

Click to expand...

Where is your work - other than trying to fill into formulae blindly?

Did you understand the statement made by Galactus -

The problem states 'within' 3 trials. So, it is poossible to get them both in two trials as well.

Click to expand...

That means you need to find numbers (probability) for success in two trials and success in three trials.

Did you read your book/class-notes at all??

( (2 C 2) (8-2 C 3-2) )/ (8 C 3)

then for two do I sub... 2 in for the 3 in the denominator?

I do try and when you have an online course with a teacher that won't e-mail you back...its hard to learn math. I have no notes and no book because its online. Worst decision of my life! I'm not good at math to begin... I'm just very frustrated and am not taking your answers and putting them in. I work through it to figure out why and how you did something...otherwise I will do bad on the tests...But you shouldn't judge me saying that I basically don't know anything. I'm struggling thats why I'm at this website.

Sorry for freaking out there but seriously.....I'm frustrated.