Question

suppose you just received a shipment of eleven 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 televisions work is 0.382
(round to three decimal places as needed.)
the probability that at least one of the two televisions does not work is
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the number of non - defective TVs

Total TVs \(n = 11\), defective TVs \(d=4\). So non - defective TVs \(n_d=11 - 4=7\)

Step2: Use the complement rule

The probability that at least one does not work \(P(X\geq1)\) is the complement of the probability that both work \(P(X = 0)\)
We know \(P(X = 0)=0.382\) (given)
By the complement rule \(P(X\geq1)=1 - P(X = 0)\)

Answer:

\(1-0.382 = 0.618\)