1. 1
   A bag contains 12 balls: 5 red, 4 blue and 3 green. A ball is picked at random.

   (a)

   Find the probability that it is red.

   [1 mark]

   • A$\frac{5}{12}$
   • B$\frac{4}{12}$
   • C$\frac{3}{12}$
   • D$\frac{7}{12}$

   (b)

   Find the probability that the ball picked is not blue.

   [1 mark]

   • A$\frac{5}{12}$
   • B$\frac{1}{3}$
   • C$\frac{2}{3}$
   • D$\frac{1}{4}$

   (c)

   Find the probability that the ball picked is green or red.

   [1 mark]

   • A$\frac{5}{12}$
   • B$\frac{1}{3}$
   • C$\frac{3}{4}$
   • D$\frac{2}{3}$

   Total for question 1: 3 marks

2. 2
   A spinner has 8 equal sections numbered 1 to 8. The spinner is spun once.

   (a)

   Find the probability that it lands on an even number.

   [2 marks]

   (b)

   Find the probability that the spinner lands on a number greater than 5.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A biased dice is rolled. The probability of rolling a 6 is 0.3, and the other five outcomes (1 to 5) are all equally likely.

   (a)

   Find the probability of rolling a 1.

   [3 marks]

   (b)

   The dice is rolled 500 times. Calculate the expected number of times a 6 is rolled.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A game uses a bag of 20 counters, each either red, yellow or green, with $P(\text{red}) = 0.35$ and $P(\text{yellow}) = 0.4$.

   (a)

   Find $P(\text{green})$, and hence find the number of green counters in the bag.

   [4 marks]

   (b)

   A counter is picked at random from the bag and replaced, and this is repeated 400 times. Calculate the expected number of times a red counter is picked, and state whether you would expect exactly this many red counters in the 400 picks, giving a reason.

   [4 marks]

   (c)

   After conducting the experiment, a green counter was picked 160 times out of the 400 trials. Calculate the relative frequency of picking green from this experiment, compare it with the theoretical probability found in part (a), and comment on whether the bag's counters may need re-counting.

   [5 marks]

   Total for question 4: 13 marks

End of questions