P5 Empirical probability and sample size Quiz: AQA Maths, Unit 5

The 20 questions

1. What is empirical probability?

   • A probability estimated from observed results of trials
   • A probability decided before any trials
   • A probability that is always exactly 0.5
   • A probability calculated from equally likely outcomes

2. As the sample size increases, what does the empirical probability tend towards?

   • A value further from the theoretical probability
   • The theoretical probability
   • Zero
   • Always 0.5

3. Why must a sample be unbiased when estimating a probability?

   • So the sample can be made smaller, which saves time and money
   • So the results reflect the true probability rather than a skewed view
   • So that the outcomes of each trial are no longer random at all
   • So that the estimated probability is always exactly 1 for every event

4. Which sample gives the more reliable estimate of a probability?

   • A larger sample of trials
   • The first trial only
   • A sample of 2 trials
   • A sample of 5 trials

5. An experiment is repeated 10 times and gives 7 successes. What is the empirical probability of success?

   • 0.07
   • 0.7
   • 7
   • 0.3

6. A fair coin is tossed 4 times and lands heads every time. What is the empirical probability of heads?

   • 0
   • 0.5
   • 1
   • 0.25

7. What can happen to an empirical probability from a small sample?

   • It is always zero
   • It becomes exactly 1
   • It always matches the theoretical probability
   • It can vary a lot from the theoretical probability

8. A fair coin has theoretical probability 0.5 of heads. Which empirical result from 1000 tosses is most likely to be close to this?

   • 0.9
   • 0.2
   • 0.1
   • 0.48

9. A biased dice is rolled 200 times and shows a 3 on 50 rolls. What is the empirical probability of a 3?

   • 1/5
   • 1/3
   • 1/2
   • 1/4

10. A drawing pin lands point up 34 times in 100 throws. What is the empirical probability of point up?

    • 0.66
    • 0.34
    • 0.5
    • 0.034

11. A survey of 60 people finds 15 chose option X. What is the empirical probability of choosing X?

    • 0.75
    • 0.25
    • 0.15
    • 0.4

12. A spinner is spun 250 times and lands red 75 times. Which value best estimates the probability of red?

    • 0.03
    • 0.25
    • 0.3
    • 0.75

13. A coin is tossed 500 times. The empirical probability of heads is 0.43 and the theoretical probability is 0.4. How many more heads occurred than the theory predicts?

    • 200
    • 15
    • 25
    • 215

14. An empirical probability from 40 trials is 0.6. How many times did the outcome occur?

    • 40
    • 60
    • 24
    • 6

15. A survey of 80 people found 20 owned a car. What is the empirical probability of owning a car?

    • 0.2
    • 0.25
    • 0.75
    • 0.4

16. Which gives the more reliable estimate of the probability of heads: 10 tosses or 1000 tosses?

    • Neither gives any information
    • Both are equally reliable
    • 10 tosses
    • 1000 tosses

17. (H) A coin is tossed 200 times and gives 0.46 as the empirical probability of heads. How many heads were there?

    • 92
    • 108
    • 46
    • 98

18. (H) Two samples estimate P(A): 0.3 from 100 trials and 0.36 from 300 trials. Which estimate is more reliable?

    • Both are equally reliable
    • 0.3 from 100 trials
    • 0.36 from 300 trials
    • Neither is reliable

19. (H) An empirical probability from 600 trials is 0.3, while the theoretical probability is 1/3. What is the difference between the two?

    • 0.333
    • 0.1
    • 0.3
    • 0.033

20. What makes a sample biased?

    • It has an even number of members in the whole sample
    • It is larger than 100 members in total
    • It does not represent the population fairly
    • It uses equal probabilities for each of its members

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