A2 June 2023 Q2

EdexcelCurrent spec5 marksDecision Analysis

2. An outdoor theatre is holding a summer gala performance. The theatre owner must decide whether to take out insurance against rain for this performance.

The theatre owner estimates that

on a fine day, the total profit will be £15 000
on a wet day, the total loss will be £20 000

Insurance against rain costs £2 000. If the performance must be cancelled due to rain, then the theatre owner will receive £16 000 from the insurer. If the performance is not cancelled due to rain, then the theatre owner will receive nothing from the insurer.

The probability of rain on the day of the gala performance is 0.2

Draw a decision tree and hence determine whether the theatre owner should take out the insurance against rain for this performance. (5)

Decision tree: decision node 9200 with branches Insure and Don’t insure (Don’t insure crossed out with a double line). Insure chance node 9200: Rain 0.2 to -6000, Fine 0.8 to 13 000. Don’t insure chance node 8000: Rain 0.2 to -20 000, Fine 0.8 to 15 000 — Mark scheme

Scheme	Marks	AO
	M1 A1 A1 M1	3.3 1.1b 3.4 3.4
The theatre owner should take out the insurance	A1	1.1b
	(5)
	(5 marks)

Notes