Question

A cooler has 12 apple juices and 15 grape juices. 9 of the apple juices are sugar free and 5 of the grape juices are sugar free. A juice is chosen at random. Given that the juice is NOT sugar free, find the probability that it is grape juice.

Answer 1

The correct answer is 3/13 on usatestprep. hope this helped.

Explanation:

Answer 2

The probability that it is grape juice, given that the juice is not sugar free is 0.769 or 76.9%

Explanation:

`P(\text{Grape }|\text{ Not sugar free})=\frac{P(\text{Grape }\cap \text{ Not sugar free})}{P(\text{Not sugar free})}`

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,

`P(\text{Grape }\cap \text{ Not sugar free})=(10)/(27)`

`P(\text{Not sugar free})=(10+3)/(27)=(13)/(27)`

Putting the values,

`P(\text{Grape }|\text{ Not sugar free})=\frac{P(\text{Grape }\cap \text{ Not sugar free})}{P(\text{Not sugar free})}=((10)/(27))/((13)/(27))=(10)/(13)=0.769`