Lesson · Grade 7 · Mathematics
Why More Trials Give a Better Estimate
- Grade 7
- Mathematics
- 1 min 27 s
- British Columbia
- BC7-MA-71
Two coins are flipped 10, 100 and 1000 times, and the experimental probability of two heads goes from 40% to 28% to 25.3%, closing in on the theoretical 25%. The video then shows why: in a small set each trial is a big share of the results, so a few lucky flips move the estimate a lot, but in a big set they barely change it.
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In one sentence
The question this lesson answers
How likely is it that two flipped coins both land on heads?
The coins do not affect each other, so these 4 outcomes are equally likely.
Transcript
What the lesson says
How likely is it that two flipped coins both land on heads?
The coins do not affect each other, so these 4 outcomes are equally likely.
Two heads is 1 of the 4, so the theoretical probability is 25 percent.
Let us test it by flipping both coins 10 times.
Two heads came up 4 times, so the experimental probability is 40 percent.
That estimate is a long way from 25 percent.
Now we flip both coins 100 times.
Two heads came up 28 times, so the estimate is 28 percent.
Now we flip both coins 1000 times.
Two heads came up 253 times, so the estimate is 25.3 percent.
Each bigger set of trials gave an estimate closer to 25 percent.
In 10 trials, each trial is 10 percent of all the results.
In 1000 trials, each trial is only 0.1 percent of all the results.
So in a big set, a few lucky flips barely change the estimate.
More trials usually bring the experimental probability closer to the theoretical probability.
Curriculum
Where this fits
- British Columbia, Grade 7
Mathematics, Data and probability: experimental probability with two independent eventsBC7-MA-71
The outcomes and strands follow the British Columbia curriculum.
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