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.