Question

Suppose you just received a shipment of fourteen televisions. 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

Answer with explanation:

Given : Total number of televisions received = 14

Number of defective televisions = 3

Probability of defective televisions :$\dfrac{3}{11}$

Now, If two televisions are randomly​ selected,  then the probability that both televisions work.

$P(0)=(1-\frac{3}{11})^2\approx0.5289$

Hence, the probability that both televisions work is 0.5289 .

The probability at least one of the two televisions does not​ work will be :-

$P(X\geq1)=1-P(0)=1-0.5289\approx0.4711$

Hence, the probability at least one of the two televisions does not​ work is 0.4711.