Answer: The probability that both televisions work is 0.5625 .
The probability at least one of the two televisions does not work is 0.4375.
Step-by-step explanation:
Given : Number of televisions received in shipment= 12
Number of defective televisions received in shipment= 3
Then proportion of defective televisions =[tex]\dfrac{3}{12}=0.25[/tex]
Using binomial probability formula, the probability of getting success in x trials is given by :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
If two televisions are randomly selected, then the probability that both televisions work will be :-
[tex]P(0)=^2C_0(0.25)^0(0.75)^2=(0.75)^2=0.5625[/tex]
The probability at least one of the two televisions does not work will be :-
[tex]P(x\geq1)=1-P(0)=1-0.5625=0.4375[/tex]
