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Vanyuwa [196]
3 years ago
15

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.
Mathematics
2 answers:
Romashka-Z-Leto [24]3 years ago
5 0

Answer:

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

Step-by-step explanation:

P(\text{Grape }|\text{ Not sugar free})=\dfrac{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})=\dfrac{10}{27}

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

Putting the values,

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

Ksenya-84 [330]3 years ago
4 0

Answer:

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

Step-by-step explanation:

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