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

   (a)

   Find the probability that the counter picked 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 counter picked is blue or green.

   [1 mark]

   • A$\frac{9}{12}$
   • B$\frac{5}{12}$
   • C$\frac{4}{12}$
   • D$\frac{7}{12}$

   (c)

   A counter is picked and replaced 60 times. Find how many times a red counter would be expected to be picked.

   [1 mark]

   • A$20$
   • B$25$
   • C$15$
   • D$30$

   Total for question 1: 3 marks

2. 2
   A biased coin is spun. The probability of landing heads is $0.35$.

   (a)

   Find the probability that the biased coin lands on tails.

   [2 marks]

   (b)

   The coin is spun 200 times. Find the expected number of times it lands on tails.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In a class of 40 students, each student studies exactly one of French, Spanish or German. The probability that a randomly selected student studies French is $0.4$, and the probability that they study Spanish is $0.25$.

   (a)

   Explain why the probability that a randomly selected student studies German is $0.35$, showing your working.

   [3 marks]

   (b)

   Find the number of students in the class who study German.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A charity runs a raffle with 250 tickets, of which 15 win a prize. A player buys 1 ticket.

   (a)

   Find the probability, as a fraction in its simplest form, that the player's ticket wins a prize.

   [4 marks]

   (b)

   The charity sells an additional 50 non-winning tickets, keeping the same 15 winning tickets. Find the probability that a player's ticket does not win a prize, giving your answer as a decimal to 3 decimal places.

   [4 marks]

   (c)

   Two players each buy one ticket from the new pool of 300 tickets, without replacement. Find the probability that neither of them wins a prize, giving your answer to 3 decimal places.

   [5 marks]

   Total for question 4: 13 marks

End of questions