A2 October 2021 Q2

EdexcelCurrent spec7 marksDecision Analysis

2. Alka is considering paying £5 to play a game. The game involves rolling two fair six-sided dice. If the sum of the numbers on the two dice is at least 8, she receives £10, otherwise she loses and receives nothing.

If Alka loses, she can pay a further £5 to roll the dice again. If both dice show the same number then she receives £35, otherwise she loses and receives nothing.

(i) Draw a decision tree to model Alka’s possible decisions and the possible outcomes.

(ii) Determine Alka’s optimal EMV and state the optimal strategy indicated by the decision tree. (7)

Decision tree: decision node 0 with branches p (play, crossed with double line) and ~p to payoff 0. Play leads to a chance node −25/72: at least 8 with probability 5/12 to payoff 5; less than 8 with probability 7/12 to a decision node −25/6. That decision node has branches stop (crossed with double line) to payoff −5, and play again to a chance node −25/6: same number with probability 1/6 to payoff 25, different number with probability 5/6 to payoff −10 — Mark scheme

Scheme	Marks	AO
	M1 B1 A1 M1 M1 A1	3.3 1.1b 1.1b 3.4 3.4 1.1b
EMV is £0 and Alka should not play the game	B1	3.2a
	(7)
	(7 marks)

Notes