Repeating an Experiment
Conduct repeated chance experiments including those with and without equally likely outcomes, observe and record the results; use frequency to compare outcomes and estimate their likelihoods.
Read this first
Do it many times. Count how often each result happens. That is the frequency.
27 heads out of 50 is close to the expected 25.
Words you need
- Frequency
- How often a result happened.
- Trial
- One go at the experiment.
- Estimate
- A close guess based on the results.
Worked example
e.g. Toss a coin 50 times. You get 27 heads. What does that tell you?
- Work out what you expected. Half of 50 is 25.
- Compare. You got 27, which is close to 25.
- Write it as a frequency. 27 out of 50.
- The coin looks fair. The results are close to expected.
More trials means the frequency gets closer to what you expect.
Practice
The pictures fade as you go. By the last few you are on your own.
1You expect 25 and get 30. Is the coin unfair?with a picture
AnswerProbably not. It is still fairly close.
2A die is rolled 60 times. How many sixes do you expect?with a picture
AnswerAbout 10.
3You get 8 reds in 20 picks. Write the frequency.with a hint
Need a hint?
Out of how many?
Answer8 out of 20.
4Would 10 trials or 200 trials give a better estimate?with a hint
Need a hint?
More trials even out the luck.
Answer200.
5You roll a die 6 times and get no sixes. Is the die unfair?on your own
AnswerNo. Six trials is far too few to tell.
6You toss 100 times and get 51 heads. Fair or not?on your own
AnswerFair. That is very close to 50.
7Why do results differ each time you try?on your own
AnswerChance varies. That is what makes it chance.
Think about it
1
Why do more trials give a better estimate?
One good answerRuns of luck get evened out.
2
Can a fair coin give 8 heads in a row?
One good answerYes. It is unlikely, but possible.
Common mistakes
Judging from a few trials.
You need many before you can say anything.
Expecting exactly half every time.
About half is what you expect.