A2 June 2022 Q3

EdexcelCurrent spec7 marksDecision Analysis

3. The table below shows the transport options, usual travel times, possible delay times and corresponding probabilities of delay for a journey. All times are in minutes.

Transport option	Usual travel time	Possible delay time	Probability of delay
Car	52	10	0.10
Car	52	25	0.02
Train	45	15	0.05
Train	45	25	0.03
Coach	55	5	0.05
Coach	55	15	0.01

(a) Draw a decision tree to model the transport options and the possible outcomes. (5)

(b) State the minimum expected travel time and the corresponding transport option indicated by the decision tree. (2)

Decision tree: decision node 46.5 with branches Car, Train and Coach; Car and Coach crossed with double lines. Car chance node 53.5: 0.88 to 52, 0.1 to 62, 0.02 to 77. Train chance node 46.5: 0.92 to 45, 0.05 to 60, 0.03 to 70. Coach chance node 55.4: 0.94 to 55, 0.05 to 60, 0.01 to 70 — Mark scheme (a)

Scheme	Marks	AO
	M1 A1 M1 M1 A1	3.3 1.1b 3.4 3.4 1.1b
	(5)

Mark scheme (b)

Scheme	Marks	AO
Minimum expected travel time is 46.5 minutes Transport option is Train	B1ft B1	3.4 2.2a
	(2)
	(7 marks)

Notes

B1ft: correct travel time from their completed tree diagram (dependent on all method marks earned in (a))

B1: deduction of correct transport option (dependent on all method marks earned in (a)) including double line through inferior options in (a) (condone cross or single line here)