MCQs / Mathematics / Relative and Expected Frequencies

Relative and Expected Frequencies MCQs — Mathematics

42 multiple-choice questions on Relative and Expected Frequencies from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

1. A shop finds that 1 in 8 customers buys a dessert. On a day with 320 customers, how many desserts should it prepare?

  1. about 32
  2. about 8
  3. about 40
  4. about 280

Answer: C) about 40

Explanation: 320 18 = 40. SLO M-09-C-08 · Application

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2. A fair die is rolled 60 times. The expected number of results greater than 4 is:

  1. 40
  2. 30
  3. 10
  4. 20

Answer: D) 20

Explanation: P(5 or 6) = 13; 60 13 = 20. SLO M-09-C-07 · Understanding

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3. A school found 45 of 300 students walk to school. If the school grows to 800 students, about how many would walk?

  1. 45
  2. 240
  3. 150
  4. 120

Answer: D) 120

Explanation: 45300 = 0.15; 0.15 800 = 120. SLO M-09-C-08 · Application

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4. A seed packet says germination rate is 0.9. How many seeds should be planted to expect about 180 plants?

  1. 90
  2. 180
  3. 200
  4. 162

Answer: C) 200

Explanation: n 0.9 = 180 Rightarrow n = 200. SLO M-09-C-08 · Application

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5. The expected frequency is the number of times we expect an event in theory. The actual (observed) frequency:

  1. is always exactly equal to it
  2. is usually close to it but not exactly equal
  3. is always larger
  4. is always smaller

Answer: B) is usually close to it but not exactly equal

Explanation: Chance causes some variation from trial to trial. SLO M-09-C-07 · Understanding

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6. A coin is tossed 1000 times and gives 512 heads. What can you conclude?

  1. The coin always lands heads
  2. The coin seems fair; 512 is close to the expected 500
  3. Tails are impossible
  4. The coin is clearly biased

Answer: B) The coin seems fair; 512 is close to the expected 500

Explanation: Small differences from the expected value are normal. SLO M-09-C-08 · Application

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7. A biased coin has P( head) = 0.6. In 150 tosses, the expected number of tails is:

  1. 75
  2. 90
  3. 60
  4. 40

Answer: C) 60

Explanation: P( tail) = 0.4; 150 0.4 = 60. SLO M-09-C-07 · Understanding

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8. A card is drawn (with replacement) 1300 times. The expected number of kings is:

  1. 1200
  2. 100
  3. 50
  4. 200

Answer: B) 100

Explanation: Expected frequency = n P = 1300 113 = 100. SLO M-09-C-07 · Understanding

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9. A fair die is rolled 900 times. The expected number of 1s or 2s is:

  1. 150
  2. 310
  3. 600
  4. 300

Answer: D) 300

Explanation: Expected frequency = n P = 900 13 = 300. SLO M-09-C-07 · Understanding

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10. In a survey of 400 people, 140 prefer tea to coffee. In a town of 60 000 people, the estimated number who prefer tea is:

  1. 21 000
  2. 39 000
  3. 6 000
  4. 14 000

Answer: A) 21 000

Explanation: 140400 = 0.35; 0.35 60,000 = 21,000. SLO M-09-C-08 · Application

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11. A bag has 3 red and 7 white beads. A bead is taken and replaced 200 times. The expected number of red beads is:

  1. 60
  2. 30
  3. 140
  4. 70

Answer: A) 60

Explanation: P( red) = 310; 200 310 = 60. SLO M-09-C-07 · Understanding

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12. A fair coin is tossed 200 times. The expected number of heads is:

  1. 110
  2. 200
  3. 50
  4. 100

Answer: D) 100

Explanation: Expected frequency = n P = 200 12 = 100. SLO M-09-C-07 · Understanding

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13. Which is the best reason for using a large sample when estimating relative frequency?

  1. It changes the probability
  2. The estimate is more reliable
  3. Small samples are not allowed
  4. The answer is always exactly the probability

Answer: B) The estimate is more reliable

Explanation: More trials reduce the effect of chance. SLO M-09-C-08 · Application

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14. A goalkeeper saved 21 of 70 penalties last season. In 30 penalties this season, the expected number of saves is:

  1. 15
  2. 9
  3. 10
  4. 21

Answer: B) 9

Explanation: 2170 = 0.3; 0.3 30 = 9. SLO M-09-C-08 · Application

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15. A card is drawn from a pack and replaced, 104 times in all. The expected number of aces is:

  1. 13
  2. 26
  3. 4
  4. 8

Answer: D) 8

Explanation: P( ace) = 452 = 113; 104 113 = 8. SLO M-09-C-07 · Understanding

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16. In a cricket season a captain won 18 of 30 tosses. Based on this, the estimated probability of winning the toss is:

  1. 0.6
  2. 0.3
  3. 0.18
  4. 0.5

Answer: A) 0.6

Explanation: 1830 = 0.6 — though for a fair coin the true probability is 0.5. SLO M-09-C-08 · Application

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17. A hospital records that 12% of patients need an X-ray. On a day with 250 patients, the expected number needing an X-ray is:

  1. 30
  2. 25
  3. 12
  4. 220

Answer: A) 30

Explanation: 250 0.12 = 30. SLO M-09-C-08 · Application

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18. At a junction, 48 of 120 cars observed turned left. Out of the next 500 cars, about how many would you expect to turn left?

  1. 300
  2. 48
  3. 200
  4. 240

Answer: C) 200

Explanation: 48120 = 0.4; 0.4 500 = 200. SLO M-09-C-08 · Application

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19. An airline finds that 4% of passengers do not turn up. For a flight with 200 booked passengers, the expected number of no-shows is:

  1. 4
  2. 8
  3. 20
  4. 192

Answer: B) 8

Explanation: 200 0.04 = 8. SLO M-09-C-08 · Application

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20. A spinner with 5 equal sectors (one red) is spun 250 times. The expected number of reds is:

  1. 50
  2. 25
  3. 125
  4. 5

Answer: A) 50

Explanation: 250 15 = 50. SLO M-09-C-07 · Understanding

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21. Two dice are rolled 180 times. The expected number of totals of 7 is:

  1. 60
  2. 30
  3. 15
  4. 150

Answer: B) 30

Explanation: Expected frequency = n P = 180 16 = 30. SLO M-09-C-07 · Understanding

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22. Two coins are tossed 400 times. The expected number of two tails is:

  1. 200
  2. 50
  3. 100
  4. 300

Answer: C) 100

Explanation: Expected frequency = n P = 400 14 = 100. SLO M-09-C-07 · Understanding

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23. A fair die is rolled 600 times. The expected number of sixes is:

  1. 100
  2. 500
  3. 200
  4. 50

Answer: A) 100

Explanation: Expected frequency = n P = 600 16 = 100. SLO M-09-C-07 · Understanding

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24. A vaccine causes a mild fever in 2 out of 25 people. If 1500 people are vaccinated, about how many may get a mild fever?

  1. 60
  2. 120
  3. 200
  4. 30

Answer: B) 120

Explanation: 225 1500 = 120. SLO M-09-C-08 · Application

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25. Records show that 3 out of every 1000 drivers in a city claim on insurance each year. An insurer has 25 000 drivers. The expected number of claims is:

  1. 3
  2. 25
  3. 750
  4. 75

Answer: D) 75

Explanation: 25,000 31000 = 75. SLO M-09-C-08 · Application

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