June 2023 Paper 2 Q16

OCR MEICurrent spec8 marksProbability

16 Research conducted by social scientists has shown that 16% of young adults smoke cigarettes.

Two young adults are selected at random.

(a) Determine the probability that one smokes cigarettes and the other doesn’t. [2]

The same research has also shown that

75% of young adults drink alcohol.
66% of young adults drink alcohol, but do not smoke cigarettes.

(b) Determine the probability that a young adult selected at random does smoke cigarettes, but does not drink alcohol. [2]

(c) A young adult who drinks alcohol is selected at random. Determine the probability that this young adult smokes cigarettes. [2]

(d) Using your answer to part (c), explain whether the event that a young adult selected at random smokes cigarettes is independent of the event that a young adult selected at random drinks alcohol. [2]

Mark scheme (a)

Scheme	Marks	AO
\(0.16 \times 0.84 \times 2\) or B(2, 0.16) or B(2, 0.84) seen or \(1 - (0.84^2 + 0.16^2)\)	M1	1.1
\(\frac{168}{625}\) or 0.2688 or 0.269 or 0.27 cao	A1	1.1
	[2]

Notes

M1: condone omission of 2
allow recovery from bracket error

A1: mark the final answer
allow SC1 for correct answer unsupported

Mark scheme (b)

Scheme	Marks	AO
\(0.75 - 0.66 = 0.09\)	M1	3.1a
\([0.16 - 0.09 =]\ 0.07\) isw	A1	1.1
	[2]

Notes

M1: allow 0.09 embedded in correct place in Venn diagram or contingency table; allow M1 for 9%

A1: allow SC1 for correct answer unsupported

Scheme	Marks	AO
\(0.12 \neq 0.16\)	M1	2.1
so not independent	A1	2.2a
	[2]