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. A) 10 13 B) 15 27 C) 2 3 D) 3 4

Answer 1

altogether there are 27 juices

probability of apple juice = 12/27

probability of grape juice = 15/27

probability of sugar free = 14/27

probability of not sugar free = 13/27

They already said the juice that is chosen is definitely NOT sugar free, so we dont need to include the probability of that because we already know it.

apple juice = 12

sugar free = 9

12 - 9 = 3 not sugar free

grape juice = 15

sugar free = 5

15 - 5 = 10 not sugar free

we need the not sugar free ones, so 3 + 10 = 13

out of 13 not sugar free, 10 are grape juice, so the probability of not sugar free grape juice = 10/13, so the answer is A)

srry if this is too long, i take too long to explain things, but i hope this still helps