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.
The Attempt at a Solution
7/10*6/9 = 7/15
7/10*3/9 = 7/30
3/10*7/9 = 1/15