S1 June 2005 Q7

EdexcelOld spec12 marksProbability

7. In a school there are 148 students in Years 12 and 13 studying Science, Humanities or Arts subjects. Of these students, 89 wear glasses and the others do not. There are 30 Science students of whom 18 wear glasses. The corresponding figures for the Humanities students are 68 and 44 respectively.

A student is chosen at random.

Find the probability that this student

(a) is studying Arts subjects, (4)

(b) does not wear glasses, given that the student is studying Arts subjects. (2)

Amongst the Science students, 80% are right-handed. Corresponding percentages for Humanities and Arts students are 75% and 70% respectively.

A student is again chosen at random.

(d) Given that this student is right-handed, find the probability that the student is studying Science subjects. (3)

Mark scheme (a)

Scheme

Marks

	Glasses	No Glasses	Totals
Science	18	12	30
Arts	27	23	50
Humanities	44	24	68
Totals	89	59	148

B1
B1

\(\mathrm{P}(\text{Arts}) = \dfrac{50}{148} = \dfrac{25}{74} = 0.338\)

M1 A1

(4)

Notes

B1 B1 50 may be seen in (a); 23 may be seen in (b)

M1 a number/148

Mark scheme (b)

Scheme	Marks
\(\mathrm{P}(\text{No glasses} / \text{Arts}) = \dfrac{\frac{23}{148}}{\frac{50}{148}} = \dfrac{23}{50} = 0.46\)	M1 A1
	(2)

Notes

M1 \(\dfrac{\text{prob}}{\text{their (a) prob}}\) or \(\dfrac{\text{number}}{\text{their } 50}\)

Mark scheme (c)

Scheme	Marks
\(\mathrm{P}(\text{Right Handed}) = \left(\dfrac{30}{148} \times 0.8\right) + \left(\dfrac{50}{148} \times 0.7\right) + \left(\dfrac{68}{148} \times 0.75\right)\)	M1 A1ft
\(= \dfrac{55}{74} = 0.743\)	A1
	(3)

Notes

M1 attempt add three prob

A1ft ft on their (a)

A1 awrt 0.743

Scheme	Marks
\(\mathrm{P}(\text{Science} / \text{Right handed}) = \dfrac{\frac{30}{148} \times 0.8}{(c)} = \dfrac{12}{55} = 0.218\)	M1 A1ft A1
	(3)
	(12 marks)