Relative frequency: more trials
The Maths Habit Handout to print
A fair coin is flipped 10 times.
How likely is exactly 5 heads?
About 25%
| Flips | 20 | 100 | 500 |
|---|---|---|---|
| Heads | 13 | 56 | 255 |
| Relative frequency | 0.65 | 0.56 | 0.51 |
A bottle top is dropped. Give the best estimate of the probability that it lands face up.
| Drops | 10 | 50 | 250 |
|---|---|---|---|
| Relative frequency | 0.6 | 0.48 | 0.44 |
A spinner is spun. Blue is counted.
| Spins | 20 | 100 | 400 |
|---|---|---|---|
| Blue | 7 | 31 | 128 |
| Relative frequency | 0.35 | 0.31 | 0.32 |
Best estimate 0.32
A player takes penalties. Goals are counted.
| Penalties | 10 | 50 | 200 |
|---|---|---|---|
| Goals | 9 | 38 | 156 |
| Relative frequency | 0.9 | 0.76 | 0.78 |
Best estimate 0.78
A spinner is spun. Blue is counted.
| Spins | 20 | 100 | 400 |
|---|---|---|---|
| Blue | 7 | 31 | 128 |
| Relative frequency | 0.35 | 0.31 | 0.32 |
Best estimate 0.32
A toy brick is dropped. It can land the right way up.
| Drops | 20 | 100 | 500 |
|---|---|---|---|
| Right way up | 13 | 54 | 245 |
| Relative frequency | 0.65 | 0.54 | 0.49 |
Best estimate 0.49
A spinner is spun. Blue is counted.
| Spins | 20 | 100 | 400 |
|---|---|---|---|
| Blue | 7 | 31 | 128 |
| Relative frequency | 0.35 | 0.31 | 0.32 |
Best estimate 0.32
A drawing pin is dropped. Point up is counted.
| Drops | 10 | 50 | 200 |
|---|---|---|---|
| Point up | 4 | 23 | 86 |
| Relative frequency | 0.4 | 0.46 | 0.43 |
Best estimate 0.43
A spinner is spun. Blue is counted.
| Spins | 20 | 100 | 400 |
|---|---|---|---|
| Blue | 7 | 31 | 128 |
| Relative frequency | 0.35 | 0.31 | 0.32 |
Best estimate 0.32
A dice is rolled. Sixes are counted.
| Rolls | 30 | 120 | 600 |
|---|---|---|---|
| Sixes | 9 | 30 | 168 |
| Relative frequency | 0.3 | 0.25 | 0.28 |
Best estimate 0.28
A spinner is spun. Blue is counted.
| Spins | 20 | 100 | 400 |
|---|---|---|---|
| Blue | 7 | 31 | 128 |
| Relative frequency | 0.35 | 0.31 | 0.32 |
Best estimate 0.32
A player shoots at a basket. Baskets scored are counted.
| Shots | 10 | 40 | 100 | 250 |
|---|---|---|---|---|
| Baskets | 6 | 22 | 61 | 150 |
| Relative frequency | 0.6 | 0.55 | 0.61 | 0.6 |
Best estimate 0.6
- Theoretical probability
- What should happen, worked out from equally likely outcomes.
- Biased
- Not fair. Some outcomes come up more than they should.
A dice is rolled 600 times. It lands on six 150 times.
Is the dice fair?
Answer sheet
A coin is flipped 10 times and lands on heads 7 times. Sam says the coin must be biased. Is Sam right?
No: too few flipsA spinner is part red and part blue. In 800 spins it lands on red 594 times. What fraction of the spinner is likely to be red?
34
A spinner is spun. Red is counted.
Find the relative frequency of red after 500 spins.0.33Spins 20 100 500 Red 7 31 165 Write down the best estimate of P(red). Why?
0.33: most spinsA coin lands on heads 340 times in 500 flips. Is it fair?
No: 0.68, not near 0.5