Answer: The probability that both televisions work is [tex]\dfrac{5}{14}.[/tex]
The probability at least one of the two televisions does not work is [tex]\dfrac{9}{14}[/tex].
Step-by-step explanation:
Given : Number of televisions received = 8
Number of defective televisions=3
Number of good television = 8-3= 5
Then , the number of ways to select any two television out of 8 = [tex]^8C_2[/tex]
The number of ways to select two working televisions out of three = [tex]^5C_2[/tex]
Now , If two televisions are randomly selected, the the probability that both televisions work
[tex]=\dfrac{^5C_2}{^8C_2}=\dfrac{\dfrac{5!}{2!3!}}{\dfrac{8!}{2!6!}}=\dfrac{\dfrac{5\times4\times3!}{2\times3!}}{\dfrac{8\times7\times6!}{2\times6!}}=\dfrac{5}{14}[/tex]
Hence, the probability that both televisions work is [tex]\dfrac{5}{14}.[/tex]
Also , the probability at least one of the two televisions does not work = 1- P( both televisions work)
[tex]=1-\dfrac{5}{14}=\dfrac{14-5}{14}\\\\=\dfrac{9}{14}[/tex]
Hence, the probability at least one of the two televisions does not work is [tex]\dfrac{9}{14}[/tex]
Answer:
A) 0.604
B) 0.396
Step-by-step explanation:
# of televisions = 14
# of defective televisions = 3
# of working televisions = 14 - 3 = 11
P(both televisions work) = 11/14 x 10/13 = 0.604
P(at least one of the two televisions does not work) = 1 - P(both televisions work)
1 - 0.604 = 0.396
