Suppose you just received a shipment of twelve televisions. three of them are defective. assuming that two televisions are randomly selected, find the following probabilities:

what is the probability that both televisons work?
what is the probability that at least one does not work?

The probability that both televisons work is 18/33.
The probability that at least one does not work is 15/33.

Let x = number of shipments, x = 12
P(defective) = 3/12
P(working) =  9/12
The probability that two randomly selected televisions are both working is:
9/12 * 8/11 = 72 / 132 or 18/33
P(2 working) = 18/33 
8/11 is used for the second selection since the number of televisions has been reduced due to the first selection.

The probability of 1 not working among the two can be solved through"
P(at least one defective among the 2) = 1 - P(2 working) 
P(at least one defective among the 2)  = 15/ 33

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