Answer to Question #106547 in Statistics and Probability for Windsor Todwong

Question

Suppose you just received a shipment of
twelve
twelve televisions.
Three
Three 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?

Answer 1

P(both televisions work) = $\frac{{9\choose2}}{{12\choose 2}} = \frac{36}{66} \approx 0.54$. This is because there are 9 televisions that work out of 12 and we are choosing 2 of them.

P(at least one of the televisions does not work) = 1-P(both televisions work) $\approx$ 1-0.54 = 0.46