1. 1
   A bag contains 12 counters: 5 red, 4 blue and 3 green counters. A counter is taken from the bag at random.

   (a)

   What is the probability that the counter is red?

   [1 mark]

   • A$\frac{5}{12}$
   • B$\frac{5}{7}$
   • C$\frac{7}{12}$
   • D$\frac{1}{3}$

   (b)

   What is the probability that the counter is green?

   [1 mark]

   • A$\frac{3}{9}$
   • B$\frac{1}{3}$
   • C$\frac{1}{4}$
   • D$\frac{1}{12}$

   (c)

   What is the probability that the counter is NOT blue?

   [1 mark]

   • A$\frac{3}{4}$
   • B$\frac{1}{3}$
   • C$\frac{4}{12}$
   • D$\frac{2}{3}$

   Total for question 1: 3 marks

2. 2
   A fair spinner is divided into 8 equal sections, numbered 1 to 8. The spinner is spun once.

   (a)

   Find the probability that the spinner lands on a prime number.

   [2 marks]

   (b)

   Find the probability that the spinner lands on a number that is even or a multiple of 3.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A jar contains only yellow and purple counters. A counter is picked from the jar at random. The probability that the counter is yellow is 0.35.

   (a)

   Find the probability that the counter is purple. Give a reason for your method.

   [3 marks]

   (b)

   There are 40 counters in the jar in total. Calculate the number of purple counters, and state whether this number would need to be recalculated if the jar were topped up with more counters of an unknown mix.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   At a fairground, players pay to roll a fair six-sided dice. A player wins a prize if they roll a 6. The game is played 300 times over a weekend.

   (a)

   Work out the expected number of times a prize is won over the 300 games, and the expected number of times a prize is not won.

   [4 marks]

   (b)

   At the end of the weekend, the stallholder finds that a prize was actually won 38 times. Calculate the relative frequency of winning as a decimal, rounded to 3 significant figures, and explain why this might not be equal to the theoretical probability of $\frac{1}{6}$.

   [4 marks]

   (c)

   Using the relative frequency found in part (b), estimate the total number of games that would need to be played, at that same relative frequency, for the stallholder to expect exactly 100 wins in total. Then state, with a reason, whether playing more games would make the relative frequency a more or less reliable estimate of the theoretical probability.

   [5 marks]

   Total for question 4: 13 marks

End of questions