1. 1
   A bag contains 7 red and 3 blue counters. A counter is picked at random, its colour noted, then replaced. A second counter is then picked at random.

   (a)

   Find the probability that both counters picked are red.

   [1 mark]

   • A$\frac{49}{100}$
   • B$\frac{9}{100}$
   • C$\frac{21}{100}$
   • D$\frac{7}{10}$

   (b)

   Find the probability that the first counter is red and the second counter is blue.

   [1 mark]

   • A$\frac{9}{100}$
   • B$\frac{49}{100}$
   • C$\frac{21}{100}$
   • D$\frac{3}{10}$

   (c)

   Find the probability that at least one of the two counters picked is blue.

   [1 mark]

   • A$\frac{21}{50}$
   • B$\frac{49}{100}$
   • C$\frac{9}{100}$
   • D$\frac{51}{100}$

   Total for question 1: 3 marks

2. 2
   In a class of 30 students, 18 study French (F), 15 study Spanish (S), and 8 study both French and Spanish.

   (a)

   Find the number of students who study neither French nor Spanish.

   [2 marks]

   (b)

   Find the probability that a randomly selected student from the class studies French only (not Spanish).

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A drawer contains 5 black socks and 3 white socks. Two socks are taken at random, one after another, without replacement.

   (a)

   Find the probability that both socks are black.

   [3 marks]

   (b)

   Find the probability that the two socks taken are one of each colour.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A survey of 50 students asked whether they play football (F), basketball (B), or neither. 22 play football, 19 play basketball, and 9 play both football and basketball.

   (a)

   Find the number of students who play neither sport.

   [4 marks]

   (b)

   Find the probability that a randomly selected student plays football only (not basketball).

   [4 marks]

   (c)

   Two students are selected at random, one after another without replacement, from the whole group of 50. Find the probability that both students selected play both football and basketball.

   [5 marks]

   Total for question 4: 13 marks

End of questions