Draw a Venn diagram to represent the information above.

Write down the number of students who study Music but not Economics.

There are 22 Economics students in total.

(i) Calculate the number of students who study Economics only.

(ii) Find the number of students who study none of these three subjects.

A student is chosen at random from the 100 that were asked above.

Find the probability that this student

(i) studies Economics;

(ii) studies Music and Chemistry but not Economics;

(iii) does not study either Music or Economics;

(iv) does not study Music given that the student does not study Economics.

(A1) for rectangle and three labelled circles (U need not be seen)

(A1) for 10 in the correct region

(A1) for 2, 7 and 5 in the correct regions

(A1) for 6 and 11 in the correct regions     (A4)

16     (A1)(ft)

Note: Follow through from their Venn diagram.

(i) \(10 + 7 + 2\)     (M1)

Note: Award (M1) for summing their 10, 7 and 2.

\(22 - 19\)

\(= 3\)     (A1)(ft)(G2)

Note: Follow through from their diagram. Award (M1)(A1)(ft) for answers consistent with their diagram irrespective of whether working seen. Award a maximum of (M1)(A0) for a negative answer.

(ii) \(22 + 11+ 5 + 6\)     (M1)

Note: Award (M1) for summing 22, and their 11, 5 and 6.

\(100 - 44\)

\(= 56\)     (A1)(ft)(G2)

Note: Follow through from their diagram. Award (M1)(A1)(ft) for answers consistent with their diagram and the use of 22 irrespective of whether working seen. If negative values are used or implied award (M0)(A0).

(i) \(\frac{{22}}{{100}}\left( {\frac{{11}}{{50}},0.22,22\% } \right)\)     (A1)(G1)

(ii) \(\frac{{5}}{{100}}\left( {\frac{{1}}{{20}},0.05,5\% } \right)\)     (A1)(ft)(A1)(G2)

Note: Award (A1)(ft) for their 5 in numerator, (A1) for denominator.

   Follow through from their diagram.

(iii) \(\frac{{62}}{{100}}\left( {\frac{{31}}{{50}},0.62,62\% } \right)\)     (A1)(ft)(A1)(G2)

Note: Award (A1)(ft) for \(100 - (22 + 11 + {\text{their }}5)\), (A1) for denominator.

   Follow through from their diagram.

(iv) \(\frac{{62}}{{78}}\left( {\frac{{31}}{{39}},0.795,79.5\% } \right)\) (0.794871...)     (A1)(ft)(A1)(G2)

Note: Award (A1)(ft) for numerator, (A1) for denominator. Follow

through from part (d)(iii) for numerator.

This question divided the candidates into two parts: those who knew how to interpret the information in a manner the led to a consistent Venn diagram and those who did not. The use of the word “only” is crucial in this regard.

Follow through to the probability part of the question was contingent on the use of the given \(n(E) = 22\) ; given information should be used in subsequent parts. As ever, conditional probability proves a trial for many.

It is recommended that candidates write probabilities as unsimplified fractions as this increase their chances of gaining follow through from previous parts.

This question divided the candidates into two parts: those who knew how to interpret the information in a manner the led to a consistent Venn diagram and those who did not. The use of the word “only” is crucial in this regard.

Follow through to the probability part of the question was contingent on the use of the given \(n(E) = 22\) ; given information should be used in subsequent parts. As ever, conditional probability proves a trial for many.

It is recommended that candidates write probabilities as unsimplified fractions as this increase their chances of gaining follow through from previous parts.

This question divided the candidates into two parts: those who knew how to interpret the information in a manner the led to a consistent Venn diagram and those who did not. The use of the word “only” is crucial in this regard.

Follow through to the probability part of the question was contingent on the use of the given \(n(E) = 22\) ; given information should be used in subsequent parts. As ever, conditional probability proves a trial for many.

It is recommended that candidates write probabilities as unsimplified fractions as this increase their chances of gaining follow through from previous parts.

This question divided the candidates into two parts: those who knew how to interpret the information in a manner the led to a consistent Venn diagram and those who did not. The use of the word “only” is crucial in this regard.

Follow through to the probability part of the question was contingent on the use of the given \(n(E) = 22\) ; given information should be used in subsequent parts. As ever, conditional probability proves a trial for many.

It is recommended that candidates write probabilities as unsimplified fractions as this increase their chances of gaining follow through from previous parts.