O-LevelMathematicsProbability4024/21 · Oct/Nov 2024 · Q117 Marks
Mia has 25 shapes. She uses their properties to sort them into groups. The table shows the number of shapes in each group. Line symmetry | Triangle | Quadrilateral 4 | 9 No line symmetry | 5 | 7
- (a)Mia takes one of the triangles at random, notes its properties and replaces it. Find the probability that it has line symmetry.[2]
- (b)Mia takes one of the 25 shapes at random, notes its properties and replaces it. She then takes a second shape at random, notes its properties and replaces it. Find the probability that both shapes are quadrilaterals.[2]
- (c)Mia takes three of the 25 shapes at random without replacement. Find the probability that only one of the shapes is a triangle with line symmetry.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [2] B1 for answer 4/9 or n/n before cancelling
- [2] B1 for 16/25 seen
- [3] M2 for k × (4/25) × (21/24) × (20/23) oe where k = 1, 2 or 3
- [3] or M1 for a/25 × b/24 × c/23 oe seen
- [3] or for 4/def × 21/def × 20/def seen
- [3] or for identifying 3 combinations
- [3] If 0 scored, SC1 for answer 5292/15625
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