Answer
$\frac{11}{57}$
Work Step by Step
If A, B and C are dependent events, then
P(A,B, and C)
= P(A)*P(B given that A occurred)*P(C given that A and B occurred)
We find the probability of not selecting grape juice if we randomly select 3 cans.
E: no grape juice.
A: apple, orange, or mango juice.
B: apple, orange, or mango juice, given that one is selected
C: apple, orange, or mango juice, given that two are selected
P(A) = $\frac{12}{20}$
P(B) =$\frac{11}{19}$
P(C) = $\frac{10}{18}$
P(E) = $\frac{12}{20}$ .$\frac{11}{19}$. $\frac{10}{18}$
=$\frac{11}{57}$