4MA0 Higher January 2016 Paper 3R Q18

EdexcelHigherOld spec7 marksMultiple Events

18 There are 100 tiles in a bag.
Each tile is marked with a number.
The table shows information about the tiles.

Number on tile	Frequency
0	2
1	68
2	7
3	13
4	10

Carmen takes at random a tile from the bag.
She records the number on the tile and then replaces the tile in the bag.
Pablo takes at random a tile from the bag.

(a) Work out the probability that Carmen takes a tile with the number 0 or the number 1 and Pablo takes a tile with a number greater than 1 (2)

All 100 tiles are in the bag.
Juan takes at random a tile from the bag without replacing it.
He then takes a second tile from the bag.

(b)

(i) Work out the probability that the number on each tile is 4

(ii) Work out the probability that the total of the numbers on the two tiles is 2

(5)

Scheme	Marks
\(\dfrac{70}{100} \times \dfrac{30}{100}\) oe	M1
\(\dfrac{21}{100}\) oe	A1
	(2)

Mark scheme (b)

(i)

Scheme	Marks
\(\dfrac{10}{100} \times \dfrac{9}{99}\) oe	M1
\(\dfrac{1}{110}\)	A1

Notes

A1: oe eg \(\dfrac{90}{9900}\) or \(0.0\dot{0}\dot{9}\)

(ii)

Scheme	Marks
\(\dfrac{2}{100} \times \dfrac{7}{99}\) or \(\dfrac{7}{100} \times \dfrac{2}{99}\) or \(\dfrac{14}{9900}\) or \(\dfrac{68}{100} \times \dfrac{67}{99}\) or \(\dfrac{4556}{9900}\) oe	M1
\(\dfrac{2}{100} \times \dfrac{7}{99} + \dfrac{7}{100} \times \dfrac{2}{99} + \dfrac{68}{100} \times \dfrac{67}{99}\) oe	M1
\(\dfrac{382}{825}\)	A1
	(5)

Notes

M1: Implies first M1

A1: oe Eg \(\dfrac{4584}{9900}\) or \(0.46\dot{3}\dot{0}\)

Accept 0.463(0303…) rounded or truncated to at least 3 dp

With replacement method

Scheme	Marks
\(\dfrac{2}{100} \times \dfrac{7}{100}\) or \(\dfrac{14}{10000}\) or \(\dfrac{68}{100} \times \dfrac{68}{100}\) or \(\dfrac{4624}{10000}\) oe	M1
\(\dfrac{2}{100} \times \dfrac{7}{100} + \dfrac{7}{100} \times \dfrac{2}{100} + \dfrac{68}{100} \times \dfrac{68}{100}\) or \(\dfrac{1163}{2500}\) or 0.4652 oe	M1

Notes

M1: Implies first M1