1. 1
   A bag contains 5 red counters, 3 blue counters and 2 green counters. A counter is drawn at random.

   (a)

   What is the probability that the counter drawn is red?

   [1 mark]

   • A$\frac{1}{2}$
   • B$\frac{3}{10}$
   • C$\frac{1}{5}$
   • D$\frac{2}{5}$

   (b)

   What is the probability that the counter drawn is not blue?

   [1 mark]

   • A$\frac{3}{10}$
   • B$\frac{7}{10}$
   • C$\frac{1}{2}$
   • D$\frac{1}{5}$

   (c)

   What is the probability that the counter drawn is red or green?

   [1 mark]

   • A$\frac{9}{10}$
   • B$\frac{1}{2}$
   • C$\frac{1}{5}$
   • D$\frac{7}{10}$

   Total for question 1: 3 marks

2. 2
   A fair coin is tossed and a fair 4-sided spinner labelled 1, 2, 3, 4 is spun.

   (a)

   List the sample space of all possible outcomes, and find the probability of getting a head and an even number.

   [2 marks]

   (b)

   Find the probability of getting a tail and a number greater than 2.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The probability that a machine produces a faulty item is 0.08. The machine produces 500 items in a day.

   (a)

   Find the expected number of faulty items produced in a day.

   [3 marks]

   (b)

   Find the probability that an item is not faulty, and hence the expected number of non-faulty items produced in a day.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   In a class of 30 students, 18 study French, 15 study Spanish, and 8 study both French and Spanish.

   (a)

   Find the number of students who study only French, only Spanish, and neither language.

   [4 marks]

   (b)

   Find the probability that a randomly selected student studies exactly one of the two languages.

   [4 marks]

   (c)

   Find the probability that a randomly selected student studies French, Spanish, or both, by first working out the number of students in each region of a Venn diagram (French only, Spanish only, both) and adding them. Show that this matches the total found by adding the individual probabilities and subtracting the overlap once.

   [5 marks]

   Total for question 4: 13 marks

End of questions