1. 1
   A school fete tombola has 200 tickets in total: 6 tickets win a large prize, 24 tickets win a small prize, and the rest win no prize. One ticket is drawn at random.

   (a)

   What is the probability that the ticket wins a large prize?

   [1 mark]

   • A0.03
   • B0.12
   • C0.15
   • D0.88

   (b)

   What is the probability that the ticket wins no prize at all?

   [1 mark]

   • A0.15
   • B0.85
   • C0.30
   • D0.97

   (c)

   If a stall sells 400 raffle tickets in the same ratio of outcomes, how many would you expect to win a prize (large or small)?

   [1 mark]

   • A24
   • B48
   • C60
   • D90

   Total for question 1: 3 marks

2. 2
   A game uses 9 cards, numbered 1 to 9, shuffled face down. A card is picked at random, its number is noted, and it is NOT replaced. A second card is then picked at random from the remaining 8.

   (a)

   Find the probability that the two cards picked, in order, both show even numbers.

   [2 marks]

   (b)

   Find the probability that the two numbers picked have a sum of 10.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A local sports club has 150 members. Each member is asked whether they play football and whether they play tennis. 55 members play football only, 35 play tennis only, 20 play both sports, and the rest play neither.

   (a)

   One member is selected at random. Find the probability that the member plays at least one of the two sports.

   [3 marks]

   (b)

   Given that a randomly selected member plays football, find the probability that they also play tennis.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A netball player takes penalty shots in training. The probability that she scores on any given shot is 0.7, independent of previous shots. She takes 3 shots in a row.

   (a)

   Find the probability that she scores on exactly two of the three shots.

   [4 marks]

   (b)

   Find the probability that she scores on at least one of the three shots.

   [4 marks]

   (c)

   The player's season target is to score 30 or more goals over 40 shots. Using her success probability of 0.7, calculate her expected number of goals over 40 shots, and show whether this meets her target, stating any shortfall.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   A weather forecasting app assigns each day one of four labels: sunny, cloudy, rainy or stormy, based on historical data for a city. Over the past 300 days, 135 were sunny, 90 were cloudy, 60 were rainy and 15 were stormy.

   (a)

   Based on this data, what is the probability that a randomly chosen day was labelled cloudy?

   [1 mark]

   • A0.15
   • B0.2
   • C0.45
   • D0.3

   (b)

   What is the probability that a randomly chosen day was NOT labelled sunny?

   [1 mark]

   • A0.55
   • B0.45
   • C0.5
   • D0.65

   (c)

   Based on this data, how many of the next 60 days would you expect to be labelled either rainy or stormy?

   [1 mark]

   • A10
   • B15
   • C12
   • D18

   Total for question 5: 3 marks

6. 6
   In an online quiz, each question has 5 answer options, only one of which is correct. A contestant guesses the answers to two questions at random, independently of each other.

   (a)

   Find the probability that the contestant answers both questions correctly.

   [2 marks]

   (b)

   Find the probability that the contestant answers exactly one of the two questions correctly.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A driving school has 90 learners. 54 passed their theory test, and of those, 40 also passed their practical test on the first attempt. Of the 36 who failed their theory test, 6 passed the practical test on the first attempt.

   (a)

   One learner is selected at random. Find the probability that they passed both the theory test and the practical test on the first attempt.

   [3 marks]

   (b)

   Given that a randomly selected learner passed the practical test on the first attempt, find the probability that they had also passed the theory test.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   A quality-assurance box at a bakery contains 10 cupcakes: 3 have a chocolate filling and the rest have a vanilla filling. An inspector removes cupcakes at random, one at a time, without replacement, to check the filling.

   (a)

   The inspector removes two cupcakes. Find the probability that both have a chocolate filling.

   [4 marks]

   (b)

   Find the probability that exactly one of the two cupcakes removed has a chocolate filling.

   [4 marks]

   (c)

   The bakery restocks the box each morning so it always contains 10 cupcakes in the same ratio of chocolate to vanilla. Across a 6-day working week, the inspector carries out this two-cupcake, without-replacement check once each day. Using your answer to part (a), find the expected number of days in the week on which both cupcakes checked have a chocolate filling, and state whether this is more or less than 1 day.

   [5 marks]

   Total for question 8: 13 marks

End of questions