18M.1.SL.TZ1.T_10

pestleMathematicsAISLPaper 118M· sl-4-5-probability-concepts-expected-numberssource ↗

A group of 60 sports enthusiasts visited the PyeongChang 2018 Winter Olympic games to watch a variety of sporting events.

The most popular sports were snowboarding (S), figure skating (F) and ice hockey (H).

For this group of 60 people:

4 did not watch any of the most popular sports,
x watched all three of the most popular sports,
9 watched snowboarding only,
11 watched figure skating only,
15 watched ice hockey only,
7 watched snowboarding and figure skating,
13 watched figure skating and ice hockey,
11 watched snowboarding and ice hockey.

Complete the Venn diagram using the given information.

[3]

Find the value of x.

[2]

Write down the value of $n\left( {\left( {F \cup H} \right) \cap S'} \right)$ .

[1]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

(A1)(A1)(A1) (C3)

Note: Award (A1) for 4 in correct place.

Award (A1) for 9, 11, 15 in correct place.

Award (A1) for 7 − x, 13 − x, 11 − x in correct place.

Accept 2, 8 and 6 in place of 7 − x, 13 − x, 11 − x.

[3 marks]

$4 + 9 + 11 + 15 + x + \left( {7 - x} \right) + \left( {11 - x} \right) + \left( {13 - x} \right) = 60$ (M1)

Note: Award (M1) for equating the sum of at least seven of the entries in their Venn diagram to 60.

$\left( {x = } \right)\,\,5$ (A1)(ft) (C2)

Note: Follow through from part (a), but only if answer is positive.

[2 marks]

34 (A1)(ft) (C1)

Note: Follow through from their Venn diagram.

[1 mark]

Examiners’ report

[N/A]