Answer
$\frac{14}{285}$
Work Step by Step
Let the events A,B and C be defined as follows:-
A: grape juice on first selection.
B: grape juice on second selection.
C: grape juice on third selection.
Clearly, we have to find P(A∩B∩C).
We can find that P(A)= $\frac{8}{20}$,
P(B|A)= $\frac{7}{19}$ and P(C|A∩B)= $\frac{6}{18}$.
By the multiplication rule of probability, we have P(A∩B∩C)= P(A)·P(B|A)·P(C|A∩B)= $\frac{8}{20}\times\frac{7}{19}\times\frac{6}{18}= \frac{14}{285}$
