1. 1
   In a Venn diagram, set A represents students who like tennis and set B represents students who like swimming, within a universal set of 40 students. Region A only contains 12 students, region B only contains 9 students, and region A∩B (both) contains 6 students.

   (a)

   How many students, out of the 40, like neither tennis nor swimming?

   [1 mark]

   • A13
   • B27
   • C6
   • D21

   (b)

   What is the probability that a randomly selected student likes both tennis and swimming?

   [1 mark]

   • A$\frac{3}{10}$
   • B$\frac{3}{20}$
   • C$\frac{9}{40}$
   • D$\frac{13}{40}$

   (c)

   What is the probability that a randomly selected student likes tennis only (not swimming)?

   [1 mark]

   • A$\frac{9}{40}$
   • B$\frac{3}{20}$
   • C$\frac{3}{10}$
   • D$\frac{13}{40}$

   Total for question 1: 3 marks

2. 2
   A box contains 4 red pens and 6 blue pens. Two pens are selected at random, one after another, without replacement.

   (a)

   Using a tree-diagram approach, find the probability that both pens selected are red.

   [2 marks]

   (b)

   Using a tree-diagram approach, find the probability that the first pen is blue and the second pen is red.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A spinner has independent probability 0.3 of landing on red on each spin. The spinner is spun twice.

   (a)

   Using a tree-diagram approach, find the probability of getting at least one red on the two spins.

   [3 marks]

   (b)

   Find the probability of getting exactly one red on the two spins.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A company tests 200 products for two defects, A and B. From a Venn diagram: 15 products have defect A only, 10 have defect B only, 5 have both defects, and the rest have neither defect.

   (a)

   Find the number of products with neither defect, and hence find the probability that a randomly selected product has no defect.

   [4 marks]

   (b)

   Given that a defective product (one with at least one defect) is selected at random, find the probability that it has both defects.

   [4 marks]

   (c)

   Two products are selected at random, without replacement, from the 200 products. Using a tree-diagram approach, find the probability that both products have no defect at all. Give your answer to 3 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions