1. 1
   A spinner has 9 equal sections numbered 1 to 9. The spinner is spun once.

   (a)

   (a) What is the probability that the spinner lands on a number greater than $6$?

   [1 mark]

   • A$\frac{4}{9}$
   • B$\frac{1}{3}$
   • C$\frac{2}{9}$
   • D$\frac{3}{10}$

   (b)

   (b) What is the probability that the spinner lands on an odd number?

   [1 mark]

   • A$\frac{4}{9}$
   • B$\frac{5}{9}$
   • C$\frac{1}{2}$
   • D$\frac{5}{18}$

   (c)

   (c) What is the probability that the spinner does NOT land on a multiple of $3$?

   [1 mark]

   • A$\frac{1}{3}$
   • B$\frac{2}{9}$
   • C$\frac{2}{3}$
   • D$\frac{7}{9}$

   Total for question 1: 3 marks

2. 2
   A vending machine at a gym contains $45$ protein bars: $18$ are chocolate flavour, $12$ are vanilla flavour, and the rest are berry flavour.

   (a)

   (a) Find the probability that a bar taken at random from the machine is berry flavour.

   [2 marks]

   (b)

   (b) The gym manager says, \"You are more likely to get a chocolate bar than a vanilla or berry bar combined.\" Determine, with a reason, whether the manager is correct.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A footballer takes two independent penalty kicks in practice. The probability that he scores on any single kick is $0.8$.

   (a)

   (a) Find the probability that he scores on both kicks.

   [3 marks]

   (b)

   (b) Find the probability that he scores on exactly one of the two kicks.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A group of $90$ students each play exactly one of hockey or netball, and each is either in Year 10 or Year 11. Of the $50$ Year 10 students, $30$ play hockey. Of the $40$ Year 11 students, $15$ play hockey.

   (a)

   (a) A student is chosen at random from the whole group. Find the probability that the student plays netball.

   [4 marks]

   (b)

   (b) Given that a randomly chosen student plays hockey, find the probability that they are in Year 11.

   [4 marks]

   (c)

   (c) Two students are chosen at random from the whole group, one after another, without replacement. Find the probability that both students play netball.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   A bag of mixed sweets contains only lemon, orange and strawberry flavours. The probability of picking a lemon sweet at random is $0.3$ and the probability of picking an orange sweet is $0.45$.

   (a)

   (a) What is the probability of picking a strawberry sweet?

   [1 mark]

   • A$0.75$
   • B$0.15$
   • C$0.55$
   • D$0.25$

   (b)

   (b) A sweet is picked and replaced $200$ times. Estimate the expected number of times an orange sweet is picked.

   [1 mark]

   • A$90$
   • B$45$
   • C$110$
   • D$60$

   (c)

   (c) Which list correctly orders the three flavours from least to most likely to be picked?

   [1 mark]

   • Alemon, strawberry, orange
   • Bstrawberry, lemon, orange
   • Corange, lemon, strawberry
   • Dstrawberry, orange, lemon

   Total for question 5: 3 marks

6. 6
   A caf\'e tested a new muffin recipe. Out of the first $50$ customers who tried it, $34$ said they liked it.

   (a)

   (a) Estimate the probability that a customer selected at random likes the new muffin, based on this sample.

   [2 marks]

   (b)

   (b) The caf\'e expects $650$ customers to try the muffin next month. Estimate how many will like it.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A drawer contains $9$ socks: $5$ black and $4$ white, all identical apart from colour. Two socks are taken out at random, one after another, without replacement.

   (a)

   (a) Find the probability that both socks are black.

   [3 marks]

   (b)

   (b) Find the probability that the two socks are different colours.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   In a survey of $70$ members of a gym, each member does at least one of two classes: spin or yoga. $42$ members do spin and $31$ members do yoga.

   (a)

   (a) Show that $3$ members do both spin and yoga.

   [4 marks]

   (b)

   (b) A member is chosen at random. Find the probability that they do yoga but not spin.

   [4 marks]

   (c)

   (c) Given that a randomly chosen member does spin, find the probability that they also do yoga.

   [5 marks]

   Total for question 8: 13 marks

End of questions