Doing It Again and Again
Conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results.
Read this first
One try tells you almost nothing. Many tries show a pattern.
Twenty tosses gave 11 heads and 9 tails. Close, but not equal.
Words you need
- Trial
- One go at an experiment.
- Result
- What happened that time.
- Variation
- How the results change each time you try.
Worked example
e.g. Toss a coin 20 times. What do you expect?
- A coin has two sides. You expect about half heads.
- Half of 20 is 10. So expect about 10 heads.
- Try it. You might get 11 heads and 9 tails.
- That is close to 10. It will rarely be exactly 10.
Do it more times. The results get closer to what you expect.
Practice
The pictures fade as you go. By the last few you are on your own.
1You expect 10 heads and get 12. Is the coin unfair?with a picture
AnswerNo. That is close enough.
2You roll a die 60 times. How many sixes do you expect?with a picture
AnswerAbout 10.
3Why not just toss the coin once?with a hint
Need a hint?
What would one toss tell you?
AnswerOne toss shows nothing about the pattern.
4Two children get different results. Who is wrong?with a hint
Need a hint?
Think about variation.
AnswerNeither. Results change each time.
5You toss 100 times. Do you expect closer to half, or further away?on your own
AnswerCloser to half.
6You get 20 heads in 20 tosses. What would you do?on your own
AnswerTry again many more times, then check the coin.
7Why do we say 'about' 10 and not exactly 10?on your own
AnswerChance varies. Exactly 10 is only one of many results.
Think about it
1
Why do more trials help?
One good answerOdd runs of luck get evened out.
2
Does a coin remember the last toss?
One good answerNo. Every toss starts fresh.
Common mistakes
Judging a coin from a few tosses.
You need many tries before you can tell.
Expecting exactly half every time.
About half is what you expect, not exactly half.