A-LevelMathematicsProbability and statistics9709/63 · May/June 2017 · Q35 Marks

A shop sells two makes of coffee, Café Premium and Café Standard. Both coffees come in two sizes, large jars and small jars. Of the jars on sale, 65% are Café Premium and 35% are Café Standard. Of the Café Premium, 40% of the jars are large and of the Café Standard, 25% of the jars are large. A jar is chosen at random.

(i)Find the probability that the jar is small.[2]
(ii)Find the probability that the jar is Café Standard given that it is large.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[M1] P(S) = 0.65 × 0.6 + 0.35 × 0.75 Summing two 2-factor probs or 1 – (sum of two 2-factor probs)
[A1] = 0.653 (261/400)
[M1] P(Std|L) = P(Std∩L) / P(L) = 0.35×0.25 / (1-0.6525) = 0.0875/0.3475 'P(Std)' × 'P(L/Std)'as num of a fraction. Could be from tree diagram in 3(i).
[M1] Denominator (1 - their (i)) or their (i) or 0.65 x 0.4(or 0.6) + 0.35 × 0.25(or 0.75) = 0.26+0.0875 or P(L) from their tree diagram
[A1] = 0.252 (35/139)

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, May/June 2017 Paper 6 Variant 3, question 3.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content