4MA0 Higher June 2012 Paper 4 Q18

EdexcelHigherOld spec6 marksTree Diagrams

18 Bill and Jo play some games of table tennis.
The probability that Bill wins the first game is 0.7
When Bill wins a game, the probability that he wins the next game is 0.8
When Jo wins a game, the probability that she wins the next game is 0.5
The first person to win two games wins the match.

(a) Complete the probability tree diagram.

Probability tree diagram for first, second and third games, with 0.7 on the Bill wins branch of the first game

(3)

(b) Calculate the probability that Bill wins the match. (3)

Mark scheme (a)

Scheme	Marks
0.3 on bottom LH branch	B1
0.8, 0.2, 0.5, 0.5	B1
0.5, 0.5, 0.8, 0.2	B1
	(3)

Notes

B1: Second game branches correct

B1: Third game branches correct

Apart from questions 5, 7, 13c, 16b, 20, 21 and 22 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.

Mark scheme (b)

Scheme	Marks
(0.7 × “0.8”)+(0.7 × ”0.2”×”0.5”)+(“0.3”×”0.5”× “0.8”)	M2 ft
0.75 oe	A1
	(3)
	(Total 6 marks)

Notes

M2 ft: M1 for 1 correct (ft) branch

Alt method (1 – Jo winning)

Scheme	Marks
1 − {(0.7×“0.2”×“0.5)+(“0.3”×“0.5”×“0.2)+(“0.3”×“0.5”)	M2
0.75 oe	A1