Higher November 2022 Paper 6 Q4

4 Sam and Taylor are playing a game against a computer.
They can win, draw or lose the game.

Sam says

I think the probability of us winning the game is 0.3.

Taylor says

I think the probability of us losing the game is 0.75.

(a) Explain why Sam and Taylor cannot both be correct. [1]

(b) Sam is correct. The probability of them winning the game is 0.3.
Taylor is not correct. The probability of them losing the game is actually 0.55.

Complete this partly drawn tree diagram to show all the possible outcomes of playing the game twice.

[3]

Mark scheme (a)

Answer	Marks	Part marks and guidance
0.3 + 0.75 [= 1.05] is greater than 1	1		Condone additional statements that do not contradict See appendix Condone 100% for 1

Comment	Reason	Mark
0.3 + 0.75 add to greater than 1		1
They add to greater than 1	Allow “they” or “the probabilities” etc for 0.3 and 0.75 (1.05 does not need to be seen)	1
0.3 + 0.75 = 1.05 which is more than 1. The probability of winning + losing should equal 1.	Winning + losing should ≤ 1 but does not contradict required evidence	1
Probabilities add up to 1 and 0.3 + 0.75 = 1.05 which is beyond 1	First vague words do not contradict required evidence	1
0.3 + 0.75 = 1.05 and probability only goes to 1	BOD “only goes to” as meaning “cannot be greater than”	1
The probabilities should add to 1 but instead 1.05 which isn’t possible	“Which isn’t possible” not enough without > 1	0
0.3 + 0.75 = 1.05 so they cannot both be correct	True but doesn’t say why they cannot both be correct (0.3 + 0.75 > 1)	0
Probabilities must add to 1 or less	True general statement but not related it to this context	0
They must add up to less than 1	Incorrect, they could also add up to 1 but have not mentioned adding to > 1	0
They must add up to 1	Incorrect, they could also add up to less than 1 but have not mentioned adding to > 1	0
0.3 + 0.75 = 1.05 and it needs to be a whole number	Sum is correct but reason does not say more than 1	0
They cannot be right because probabilities must add to 1 which they don’t	Probabilities do not always add to 1 and the required evidence is not given	0

Mark scheme (b)

Answer	Marks	Part marks and guidance
Correct tree diagram	3	B1 for P(draw) = 0.15 B1 for two correctly placed sets of three branches with win/draw/lose labels B1 for 0.3, their 0.15 and 0.55 correctly placed on all branches	May be on diagram or in a calculation e.g. 0.3 + 0.55 + 0.15 = 1 oe Ignore probabilities Accept e.g. W/D/L as labels Condone omission of their 0.15 on printed branches