Higher June 2025 Paper 6 Q25

25 A bag contains only round tiles and square tiles.
Each tile is either black or white.

The ratio of round tiles to square tiles is 3 : 1.
45% of all the tiles are round black tiles.
9% of all the tiles are square white tiles.

Show that the proportion of round tiles that are black is less than the proportion of square tiles that are black. [6]

Answer	Marks	Part marks and guidance
Proportion of black given round found as 0.6 oe and Proportion of black given square found as 0.64 oe	B5	B4 Proportion of black given round found as 0.6 oe or Proportion of black given square found as 0.64 oe or B3 Number or proportion of square black tiles found or M1 Round to square ratio of 3 : 1 used productively M1 Number or proportion of round black and square white found (or, in the percentage method only 25 – 9 oe)	All values may be seen in working or in diagrams/tables
0.6 < 0.64 oe with both in comparable form	B1dep

%	Black	White	Total
Round	0.45		0.75
Square	0.16	0.09	0.25
Total			1

Freq.	Black	White	Total
Round	90		150
Square	32	18	50
Total			200

%	Black	White	Total
Round	45		75
Square	16	9	25
Total			100