1. 1
   A bag contains 20 sweets: 8 strawberry, 5 lime and 7 orange. One sweet is picked at random.

   (a)

   What is the probability that the sweet is lime?

   [1 mark]

   • A1/4
   • B5/8
   • C2/5
   • D1/5

   (b)

   What is the probability that the sweet is NOT orange?

   [1 mark]

   • A7/20
   • B13/20
   • C1/20
   • D3/20

   (c)

   If a sweet is picked, its colour noted, and put back, and this is repeated 60 times, what is the expected number of times a strawberry sweet is picked?

   [1 mark]

   • A8
   • B15
   • C24
   • D21

   Total for question 1: 3 marks

2. 2
   A drawer contains 9 pens: 4 blue and 5 black. Two pens are taken at random, one after another, without replacement.

   (a)

   Find the probability that the first pen taken is blue.

   [2 marks]

   (b)

   Find the probability that both pens taken are blue.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A spinner is divided into 3 equal sections coloured red, green and yellow. The spinner is spun twice.

   (a)

   Find the probability that both spins land on the same colour.

   [3 marks]

   (b)

   Find the probability that at least one of the two spins lands on red.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A school records data for 80 students on whether they attended revision classes and whether they passed their exam. Of the 80 students, 50 attended revision classes, and 42 of those who attended revision classes passed. Of the 30 students who did not attend revision classes, 12 passed.

   (a)

   Find the probability that a randomly selected student passed their exam.

   [4 marks]

   (b)

   Given that a student did not attend revision classes, find the probability that they failed their exam.

   [4 marks]

   (c)

   Two students are selected at random from the 80, one after another, without replacement. Find the probability that both selected students attended revision classes and passed their exam.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   A box contains 25 tokens: 10 gold, 9 silver and 6 bronze. One token is picked at random.

   (a)

   What is the probability that the token is silver?

   [1 mark]

   • A6/25
   • B2/5
   • C3/5
   • D9/25

   (b)

   What is the probability that the token is gold or bronze?

   [1 mark]

   • A16/25
   • B9/25
   • C19/25
   • D10/25

   (c)

   If a token is picked, noted, and put back, and this is repeated 150 times, what is the expected number of bronze tokens picked?

   [1 mark]

   • A54
   • B36
   • C6
   • D25

   Total for question 5: 3 marks

6. 6
   A charity shop has a box of 12 umbrellas: 5 are black and 7 are colourful. Two umbrellas are sold at random, one after another, without replacement.

   (a)

   Find the probability that the first umbrella sold is colourful.

   [2 marks]

   (b)

   Find the probability that both umbrellas sold are colourful.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   On any given day in autumn, the probability of rain at a weather station is 0.4. If it rains, the probability that a scheduled outdoor concert is cancelled is 0.75. If it does not rain, the probability that the concert is cancelled (for other reasons) is 0.1.

   (a)

   Find the probability that it rains AND the concert is cancelled.

   [3 marks]

   (b)

   Find the overall probability that the concert is cancelled.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   A factory tests a batch of 100 circuit boards for two faults: a wiring fault (W) and a soldering fault (S). Of the 100 boards, 18 have a wiring fault, 25 have a soldering fault, and 8 have both faults.

   (a)

   Find the probability that a randomly selected board has a wiring fault but NOT a soldering fault.

   [4 marks]

   (b)

   Find the probability that a randomly selected board has neither fault.

   [4 marks]

   (c)

   Given that a board has a soldering fault, find the probability that it also has a wiring fault. Then, two boards are selected at random from the 100, one after another, without replacement; find the probability that both have a soldering fault.

   [5 marks]

   Total for question 8: 13 marks

End of questions