Suppose you just received a shipment of six televisions. four of the televisions are defective. if two televisions are randomly selected, compute the probability that both televisions work. what is the probability at least one of the two televisions does not work?

The probability that both TVs work is 1/15. 
The probability that at least one does not work is 14/15.

Explanation
4/6 of the TVs are defective, and 2/6 are working.  The probability that two TVs drawn from this sample would be working is given by

2/6(1/5) = 2/30 = 1/15.  Getting one that works the first time changes the probability of the second one working.

The probability that at least one of them is defective is the same as 1 minus the probability that neither of them are defective.  This probability was 1/15; then we have

1-1/15 = 14/15.