Question
You are sailing from one island to another. Uninterrupted travel between the two islands takes $12$ minutes. However, there are $5$ wave checks between the islands. Four of the wave checks will stop you with $25\%$ probability each. These wave checks will add $1$ minute to your total travel time if you are stopped. However, the last wave check stops you with $75\%$ probability. This wave check will add $4$ minutes to your travel time if you are stopped. Find the expected duration (in minutes) of the trip between the two islands.