Question 9

9.1 A survey was done among 80 learners on their favourite sport

The results are shown below :

• 52 learners like rugby (R)
• 42 learners like volleyball(V)
• 5 learners like chess (C)
• 14 learners like rugby and volleyball but not chess
• 12 learners like rugby and chess but not volleyball
• 15 learners like volleyball and chess but not rugby
• 𝑥 learners like all 3 types of sport
• 3 learners do not like any sport

9.1 Draw a Venn diagram to represent the information above. (5)

9.2 Show that 𝑥 = 8 (2)

9.3 How many like only rugby ? (1)

9.4 Calculate the probability that a learner, chosen randomly, likes at least TWO different types of sport (3)

[11]

TOTAL: 150