Answer:
We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.
Explanation:
We know that the probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next.
Therefore, we get p=0.2 and q=1-p=1-0.2=0.8.
So we will calculate the probability that the buyer will not win the prize in the first and second bottles. We get:

We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.