Answer:
The probability that it is grape juice, given that the juice is not sugar free is 0.769 or 76.9%
Step-by-step explanation:
[tex]P(\text{Grape }|\text{ Not sugar free})=\dfrac{P(\text{Grape }\cap \text{ Not sugar free})}{P(\text{Not sugar free})}[/tex]
A cooler has 12 apple juices and 15 grape juices. So total 27 juices are there.
Out of 12 apple juices, 9 of the apple juices are sugar free, so 3 are not sugar free.
Out of 15 grape juices, 5 of the grape juices are sugar free, so 10 are not sugar free. So,
[tex]P(\text{Grape }\cap \text{ Not sugar free})=\dfrac{10}{27}[/tex]
[tex]P(\text{Not sugar free})=\dfrac{10+3}{27}=\dfrac{13}{27}[/tex]
Putting the values,
[tex]P(\text{Grape }|\text{ Not sugar free})=\dfrac{P(\text{Grape }\cap \text{ Not sugar free})}{P(\text{Not sugar free})}=\dfrac{\frac{10}{27}}{\frac{13}{27}}=\dfrac{10}{13}=0.769[/tex]
