Answer
$\frac{91}{285}$
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 apple juice if we randomly select 3 cans.
E: no apple juice
A: grape, orange, or mango juice.
B: grape, orange, or mango juice, given that one is selected
C: grape, orange, or mango juice, given that two are selected
P(A) = $\frac{14}{20}$
P(B) =$\frac{13}{19}$
P(C) = $\frac{12}{18}$
P(E) = $\frac{14}{20}$ .$\frac{13}{19}$. $\frac{12}{18}$
=$\frac{91}{285}$
