Question

Suppose you just received a shipment of 7 televisions. 4 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?

1. The probability that both televisions work is ______

Answer 1

$$P(both \ work)=\dfrac{\dbinom{3}{2}\dbinom{4}{0}}{\dbinom{7}{2}}$$

$$=\dfrac{\dfrac{3!}{2!(3-2)!}\cdot1}{\dfrac{7!}{2!(7-2)!}}=\dfrac{3}{21}=\dfrac{1}{7}$$

$$P(at\ least\ 1 \ does\ not\ work)$$

$$=1-P(both \ work)=1-\dfrac{1}{7}=\dfrac{6}{7}$$