(a) Over a long period of time, it is found that the probability of a train from Bewford to London being late is 0.2.
(i) One morning there are two trains from Bewford to London. Use the information to complete the tree diagram.
[2]
(ii) Work out the probability that both trains are not late. [2]
(iii) Give a reason why the probabilities used in the tree diagram for the second train may not be reliable. [1]
(b) Morgan takes a train from London to Bewford and then another train to Agon. The tree diagram shows the probabilities of Morgan’s trains being late or not late.
Morgan will not catch the train to Agon if the train to Bewford is late and the train to Agon is not late.
Work out the probability that Morgan will catch the train to Agon. [3]
Mark scheme (a)
Answer
Marks
Part marks and guidance
(i) 0.2 and 0.8 in all the correct places
2
B1 for first branch correct or second branches correct
Accept equivalent fractions and percentages (need % sign)
(ii) 0.64 or \(\dfrac{16}{25}\) oe or 64%
2
FTtheir tree for 1 or 2 marks (their values \(\lt 1\)) M1 for \(0.8 \times 0.8\) oe
Allow long method: e.g. \(1 - (0.04 + 0.16 + 0.16)\)
(iii) Suggestion of dependence between the trains
or unexpected events
or data may not be applicable
1
Accept any correct reason, e.g. if first train is late second train may be held up e.g. unexpected delays can occur e.g. changed schedule that day (implies data not applicable)
Mark scheme (b)
Answer
Marks
Part marks and guidance
0.73[4] or \(\dfrac{734}{1000}\) oe or 73.4%
3
M2 for \(1 - 0.35 \times 0.76\) or \(0.35 \times 0.24 + 0.65 \times 0.24 + 0.65 \times 0.76\) oe or M1 for two correct products or \(0.35 \times 0.76\)
