1. 1
   A group of 40 students were asked if they own a bicycle. 25 own a bicycle, and of those, 10 also own a scooter. Of the 15 who do not own a bicycle, 6 own a scooter.

   (a)

   Given that a randomly selected student owns a bicycle, find the probability they also own a scooter.

   [1 mark]

   • A$\frac{2}{5}$
   • B$\frac{10}{40}$
   • C$\frac{5}{8}$
   • D$\frac{3}{5}$

   (b)

   Given that a randomly selected student owns a scooter, find the probability they also own a bicycle.

   [1 mark]

   • A$\frac{10}{40}$
   • B$\frac{2}{5}$
   • C$\frac{5}{8}$
   • D$\frac{3}{8}$

   (c)

   Find the probability that a randomly selected student owns neither a bicycle nor a scooter.

   [1 mark]

   • A$\frac{10}{40}$
   • B$\frac{6}{40}$
   • C$\frac{15}{40}$
   • D$\frac{9}{40}$

   Total for question 1: 3 marks

2. 2
   A box contains 6 milk chocolates and 4 dark chocolates. Two chocolates are taken at random, one after another, without replacement.

   (a)

   Given that the first chocolate taken is milk, find the probability that the second chocolate is also milk.

   [2 marks]

   (b)

   Given instead that the first chocolate taken is dark, find the probability that the second chocolate is milk.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Data collected on 60 days show: 15 days it rained and the match was postponed; 5 days it rained and the match was not postponed; 3 days it did not rain but the match was postponed; 37 days it did not rain and the match was not postponed.

   (a)

   Given that it rained, find the probability the match was postponed.

   [3 marks]

   (b)

   Given that the match was not postponed, find the probability that it did not rain.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A committee of 12 people contains 7 women and 5 men. Two people are selected at random, one after another, without replacement, to be chair and vice-chair.

   (a)

   Given that the chair selected is a woman, find the probability that the vice-chair selected is also a woman.

   [4 marks]

   (b)

   Find the probability that both the chair and vice-chair selected are women.

   [4 marks]

   (c)

   Given that at least one of the chair and vice-chair selected is a man, find the probability that both are men.

   [5 marks]

   Total for question 4: 13 marks

End of questions