Find the probability distribution

[Sucks@Physics]

Homework Statement

A box of 10 flashbublbs contains 3 defective bublbs. A random sample of 2 is selcted and tested. Let X be the radom variable associated with the number of defective bulbs in the sample.

A) Find the probability distribution of X.

B) Find the expected number of defective bulbs in a sample.

I did this problem, I got 7/15 probability of there being no defective light bulbs, 1/15 of there being 2, but I got 7/30 of there being 1. The 7/30 is wrong but I don't know where I'm going wrong, please give me some help. Thanks in advance.

Homework Equations

The Attempt at a Solution

7/10*6/9 = 7/15
7/10*3/9 = 7/30
3/10*7/9 = 1/15

 

[tiny-tim]

7/10*6/9 = 7/15
7/10*3/9 = 7/30
3/10*7/9 = 1/15

Hi Sucks@Physics !

(in the last line, you wrote a 7 instead of a 2 )

As you've probably noticed, the three probabilities should add up to 1.

Your 7/30 is the probability of the first one being defective, and the second one good … but you also need the probability of the first one being good, and the second one defective … that doubles it!