AQA S1 2015 June — Question 3 4 marks

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2015
SessionJune
Marks4
TopicProbability Definitions
TypeSequential events and tree diagrams

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.
  1. Complete the table.
  2. Write down the probability that, on a particular day, the ferry:
    1. both departs and arrives on time;
    2. departs late.
  3. Find the probability that, on a particular day, the ferry:
    1. arrives late, given that it departed late;
    2. does not arrive late, given that it departed on time.
  4. 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]
  5. \begin{table}[h]
    \captionsetup{labelformat=empty} \caption{Answer space for question 3}
    \multirow{2}{*}{}Arrive at A
    EarlyOn timeLateTotal
    \multirow{2}{*}{Depart from D}On time0.160.560.08
    Late
    Total0.220.651.00
    \end{table}