3 A ferry sails once each day from port D to port A. The ferry departs from D on time or late but never early. However, the ferry can arrive at A early, on time or late.
The probabilities for some combined events of departing from \(D\) and arriving at \(A\) are shown in the table below.
- Complete the table.
- Write down the probability that, on a particular day, the ferry:
- both departs and arrives on time;
- departs late.
- Find the probability that, on a particular day, the ferry:
- arrives late, given that it departed late;
- does not arrive late, given that it departed on time.
- On three particular days, the ferry departs from port D on time.
Find the probability that, on these three days, the ferry arrives at port A early once, on time once and late once. Give your answer to three decimal places.
[0pt]
[4 marks] - \begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Answer space for question 3}
| \multirow{2}{*}{} | Arrive at A | |
| | Early | On time | Late | Total |
| \multirow{2}{*}{Depart from D} | On time | 0.16 | 0.56 | 0.08 | |
| Late | | | | |
| Total | 0.22 | 0.65 | | 1.00 |
\end{table}