Answer: The probability that both televisions work is ![\dfrac{5}{14}.](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B14%7D.)
The probability at least one of the two televisions does not work is
.
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 = ![^8C_2](https://tex.z-dn.net/?f=%5E8C_2)
The number of ways to select two working televisions out of three = ![^5C_2](https://tex.z-dn.net/?f=%5E5C_2)
Now , If two televisions are randomly selected, the the probability that both televisions work
![=\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}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5E5C_2%7D%7B%5E8C_2%7D%3D%5Cdfrac%7B%5Cdfrac%7B5%21%7D%7B2%213%21%7D%7D%7B%5Cdfrac%7B8%21%7D%7B2%216%21%7D%7D%3D%5Cdfrac%7B%5Cdfrac%7B5%5Ctimes4%5Ctimes3%21%7D%7B2%5Ctimes3%21%7D%7D%7B%5Cdfrac%7B8%5Ctimes7%5Ctimes6%21%7D%7B2%5Ctimes6%21%7D%7D%3D%5Cdfrac%7B5%7D%7B14%7D)
Hence, the probability that both televisions work is ![\dfrac{5}{14}.](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B14%7D.)
Also , the probability at least one of the two televisions does not work = 1- P( both televisions work)
![=1-\dfrac{5}{14}=\dfrac{14-5}{14}\\\\=\dfrac{9}{14}](https://tex.z-dn.net/?f=%3D1-%5Cdfrac%7B5%7D%7B14%7D%3D%5Cdfrac%7B14-5%7D%7B14%7D%5C%5C%5C%5C%3D%5Cdfrac%7B9%7D%7B14%7D)
Hence, the probability at least one of the two televisions does not work is ![\dfrac{9}{14}](https://tex.z-dn.net/?f=%5Cdfrac%7B9%7D%7B14%7D)