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 NOT grape juice. A) 1 4 B) 10 13 C) 2 3 D) 3 13

Answer 1

A - juice is not sugar free

B - juice is not grape juice

$|\Omega|=27\\ |A|=13\\ |A\cap B|=3\\\\ P(A)=\dfrac{13}{27}\\ P(A\cap B)=\dfrac{3}{27}=\dfrac{1}{9}\\\\ P(B|A)=\dfrac{\dfrac{1}{9}}{\dfrac{13}{27}}=\dfrac{1}{9}\cdot\dfrac{27}{13}=\dfrac{3}{13}$

So, it's D, assuming "3 13" meant $\dfrac{3}{13}$