More Trials, Closer Results
Conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials.
Read this first
The more times you try, the closer the results get to what you expect.
With 10 tosses you might get 7 heads. With 1000 you get near half.
Words you need
- Trial
- One go at an experiment.
- Simulation
- Copying a real situation to see what happens.
- Variation
- How much the results change.
Worked example
e.g. Toss a coin 10 times, then 100, then 1000. What changes?
- With 10 tosses you might get 7 heads. That is 70%.
- With 100 tosses you might get 54. That is 54%.
- With 1000 you might get 503. That is 50.3%.
- The results settle closer to half as the trials go up.
- That is why simulations use hundreds of trials.
A few trials prove nothing. Many trials show the real pattern.
Practice
The pictures fade as you go. By the last few you are on your own.
1Which result is closest to expected?with a picture
AnswerThe 1000 trial one.
2You roll a die 600 times. How many sixes do you expect?with a picture
AnswerAbout 100.
3You get 3 heads in 4 tosses. Is the coin unfair?with a hint
Need a hint?
How many trials is that?
AnswerNo. Four trials tells you nothing.
4Why use a computer for a simulation?with a hint
Need a hint?
How long would 10 000 tosses take by hand?
AnswerIt can run thousands of trials quickly.
5You get 520 heads in 1000. Is the coin fair?on your own
AnswerYes. That is very close to half.
6Does a coin remember the last toss?on your own
AnswerNo. Every toss starts fresh.
7What happens to variation as trials increase?on your own
AnswerIt gets smaller.
Think about it
1
Why do results settle down with more trials?
One good answerRuns of luck cancel each other out.
2
Can 1000 trials still be a little off?
One good answerYes, but only a little.
Common mistakes
Trusting a small number of trials.
Ten results can look nothing like the truth.
Expecting exactly half.
About half is what you expect, not exactly half.