Draw a Venn diagram to represent the given information using sets labelled C, M and P. Complete the diagram to include the number of families represented in each region.

Find the number of families who

(i) went to the circus only;

(ii) went to the museum and the park but not the circus;

(iii) did not go to any of the three places on the weekend.

A family is chosen at random from the group of 40 families. Find the probability that the family went to

(i) the circus;

(ii) two or more places;

(iii) the park or the circus, but not the museum;

(iv) the museum, given that they also went to the circus.

Two families are chosen at random from the group of 40 families.

Find the probability that both families went to the circus.

     (A1)(A1)(A1)(A1)

Award (A1) for 3 intersecting circles and rectangle, (A1) for 1, 3, 4 and 7, (A1) for 2, (A1) for 6 and 5.

(i) 2     (A1)(ft)

(ii) 6     (A1)(ft)

(iii) 40 − (1 + 6 + 2 + 3 + 4 + 7 + 5)     (M1)

Note: Award (M1) for subtracting all their values from 40.

= 12     (A1)(ft)(G2)

Note: Follow through from their Venn diagram for parts (i), (ii) and (iii).

(i) \(\frac{{16}}{{40}}\left( {\frac{2}{5},0.4,40\% } \right)\)     (A1)(A1)(G2)

Note: Award (A1) for numerator, (A1) for denominator. Answer must be less than 1 otherwise award (A0)(A0). Award (A0)(A0) if answer is given as incorrect reduced fraction without working.

(ii) \(\frac{{20}}{{40}}\left( {\frac{1}{2},0.5,50\% } \right)\)     (A1)(ft) (A1) (G2)

Note: Award (A1)(ft) for numerator, (A1) for denominator. Follow through from their Venn diagram. Answer must be less than 1 otherwise award (A0)(A0). Award (A0)(A0) if answer is given as incorrect reduced fraction without working.

(iii) \(\frac{6}{{40}}\left( {\frac{3}{{20}},0.15,15\% } \right)\)     (A1)(ft)(A1)(G2)

Note: Award (A1)(ft) for numerator, (A1) for denominator. Follow through from their Venn diagram. Answer must be less than 1 otherwise award (A0)(A0). Award (A0)(A0) if answer is given as incorrect reduced fraction without working.

(iv) \(\frac{{11}}{{16}}\left( {0.6875,68.75\% } \right)\)     (A1)(ft)(A1)(G2)

Note: Award (A1)(ft) for numerator, (A1) for denominator. Follow through from their Venn diagram. Answer must be less than 1 otherwise award (A0)(A0). Award (A0)(A0) if answer is given as incorrect reduced fraction without working.

\(\frac{{16}}{{40}} \times \frac{{15}}{{39}}\)     (A1)(A1)(ft)

Note: Award (A1) for multiplication of their probabilities, (A1)(ft) for their correct probabilities.

\(\frac{{240}}{{1560}}\left( {\frac{2}{{13}},0.153846...,15.4\% } \right)\)     (A1)(ft)(G2)

Note: Follow through from their answer to part (c)(i). Answer must be less than 1 otherwise award at most (A1)(A1)(A0)(ft).