Estimating probabilities from experiments, judging fairness, and listing outcomes for two events.
What you will learn
- Work out and use relative frequency
- Judge whether something is fair from results
- List outcomes in a sample space
- Count choices with the product rule
Relative frequency
When you cannot work out a probability from equally likely outcomes, estimate it from an experiment: relative frequency = number of times it happened ÷ number of trials.
More trials give a more reliable estimate. If a fair coin gives 7 heads in 10 throws, that is not evidence of bias; 700 in 1000 would be. So with only a few trials, the honest conclusion is "too few to tell". When several people do the same experiment, the one with the most trials gives the most reliable estimate.
To predict, use the relative frequency as the probability: if 30 out of 200 bulbs fail, the relative frequency is 30/200 = 3/20, so about 3/20 × 1000 = 150 out of 1000 would fail.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- Relative frequency
- Sample spaces
- Try it: First question
8 practice questions, marked as you go; about 20 minutes in all.
Key terms
Sample space
In this unit: Probability
Probabilities of single events, relative frequency, sample spaces, Venn diagrams and two-way tables, tree diagrams, and conditional probability.
- Probability basics
- Relative frequency and listing outcomes
- Venn diagrams, two-way tables and frequency trees
- Tree diagrams
- Conditional probability