1. 1
   The probability that Ali passes his driving test is 0.7. The probability that Sara passes her driving test is 0.6. The two events are independent.

   (a)

   What is the probability that both Ali and Sara pass their driving tests?

   [1 mark]

   • A0.42
   • B1.3
   • C0.1
   • D0.13

   (b)

   What is the probability that neither Ali nor Sara passes?

   [1 mark]

   • A0.58
   • B0.7
   • C0.3
   • D0.12

   (c)

   What is the probability that exactly one of them passes?

   [1 mark]

   • A0.12
   • B0.42
   • C0.46
   • D1.3

   Total for question 1: 3 marks

2. 2
   In a survey of 50 people, 30 own a car and 20 do not. Of those who own a car, 18 also own a bicycle. Of those who do not own a car, 12 own a bicycle.

   (a)

   Find the probability that a person owns a bicycle, given that they own a car.

   [2 marks]

   (b)

   Find the overall probability that a randomly selected person owns a bicycle.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A bag contains 7 red balls and 3 blue balls. Two balls are drawn at random, one after another, without replacement.

   (a)

   Find the probability that both balls drawn are red.

   [3 marks]

   (b)

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

   [3 marks]

   Total for question 3: 6 marks

4. 4
   In a group of 80 gym members, the probability that a randomly selected member does weights training is 0.55, the probability they do cardio training is 0.45, and the probability they do both is 0.25.

   (a)

   Find the probability that a randomly selected member does weights training, cardio training, or both.

   [4 marks]

   (b)

   Find the number of members who do neither weights nor cardio training.

   [4 marks]

   (c)

   Find the conditional probability that a member does cardio training, given that they do weights training. Give your answer to 3 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions