The Law of Large Numbers: 100 Trials and Beyond (Year 10)
Free printable NZ Year 10 maths worksheet: a 1000-toss coin experiment and a 1000-spin spinner experiment showing relative frequency settling towards theoretical probability.
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Grade 9 · Math worksheet
Name
Date
Math
The Law of Large Numbers: 100 Trials and Beyond
A class tossed a coin and kept a running total of heads, recorded in the table at 100, 200, 500 and 1000 tosses. Use the table for the coin questions, then the spinner experiment described in the later questions.
| Number of tosses | Number of heads |
|---|---|
| 100 | 59 |
| 200 | 110 |
| 500 | 268 |
| 1000 | 490 |
- 1.What is the theoretical probability that a fair coin lands on heads? Give your answer as a decimal.
- 2.Using the table, calculate the relative frequency of heads after 100 tosses. Give your answer as a decimal.
- 3.Using the table, calculate the relative frequency of heads after 500 tosses. Give your answer as a decimal.
- 4.Using the table, calculate the relative frequency of heads after 1000 tosses. Give your answer as a decimal.
- 5.Using the table, which number of tosses gave a relative frequency closest to the theoretical probability of 0.5?
- 6.The table shows the relative frequency of heads settling towards 0.5 as the number of tosses grows. According to the Law of Large Numbers, what happens to the relative frequency of an outcome as the number of trials increases?
- a) The relative frequency gets closer to the theoretical probability
- b) The relative frequency moves further from the theoretical probability
- c) The coin becomes more likely to land heads
- d) The relative frequency stays exactly the same
- 7.A spinner has 4 equal sectors and exactly 1 of them is red. What is the theoretical probability that one spin lands on red? Give your answer as a decimal.
- 8.The spinner was spun 400 times and landed on red 112 times. Calculate the relative frequency of red. Give your answer as a decimal.
- 9.The experiment continued to 1000 spins, with 265 landing on red in total. Calculate the relative frequency of red after 1000 spins. Give your answer as a decimal.
- 10.Which estimate of the probability of red is closer to the theoretical 0.25: the relative frequency after 400 spins (112 reds) or after 1000 spins (265 reds)?
- 11.If the spinner exactly matched its theoretical probability, how many of the 1000 spins would have landed on red?
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