1. 1
   A box contains 10 pens: 6 blue and 4 black. Two pens are picked at random, one after another, without replacement.

   (a)

   Find the probability that both pens picked are blue.

   [1 mark]

   • A$\frac{1}{3}$
   • B$\frac{3}{5}$
   • C$\frac{6}{10}$
   • D$\frac{2}{15}$

   (b)

   Find the probability that the first pen picked is blue and the second is black.

   [1 mark]

   • A$\frac{1}{3}$
   • B$\frac{4}{15}$
   • C$\frac{6}{25}$
   • D$\frac{2}{9}$

   (c)

   Find the probability that at least one of the two pens picked is black.

   [1 mark]

   • A$\frac{1}{2}$
   • B$\frac{1}{3}$
   • C$\frac{4}{15}$
   • D$\frac{2}{3}$

   Total for question 1: 3 marks

2. 2
   In a survey of 80 people, 50 own a car and 45 own a bicycle. 20 people own both a car and a bicycle.

   (a)

   Find the number of people who own neither a car nor a bicycle.

   [2 marks]

   (b)

   Find the probability that a randomly selected person owns exactly one of the two (a car or a bicycle, but not both).

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A doctor's surgery finds that 30% of patients who come in have flu. Of those with flu, 80% have a fever. Of those without flu, 10% have a fever.

   (a)

   Find the probability that a randomly selected patient has flu and a fever.

   [3 marks]

   (b)

   Given that a patient has a fever, find the probability that they have flu, giving your answer to 3 decimal places.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A factory produces phone screens using two machines, Machine A and Machine B. Machine A produces 60% of the screens and Machine B produces 40%. 5% of screens from Machine A are defective, and 8% of screens from Machine B are defective.

   (a)

   Find the probability that a randomly selected screen is defective.

   [4 marks]

   (b)

   Given that a randomly selected screen is defective, find the probability that it was produced by Machine B, giving your answer to 3 decimal places.

   [4 marks]

   (c)

   The factory inspects two randomly selected screens from the day's output. Find the probability that exactly one of the two screens is defective, giving your answer to 3 decimal places.

   [5 marks]

   Total for question 4: 13 marks

End of questions