Counting what happened
Show on a big screenYou toss a coin twenty times before cricket practice starts.
- Twenty tosses, tallied five at a time.
- Heads: 12 tally marks.
- Tails: 8 tally marks.
- Chance of heads = 12/20 = 0.6.
One toss, written down
Trial — one try of the experiment. Each toss is a trial. Outcome — the result of one trial: heads or tails. Write every trial down, so nothing is guessed. A tally is a row of marks, one per toss.
The count over the whole
An observed chance comes from the tally. It is heads over every toss made. "Over" here means divided by. Experimental probability — a chance found from real trials. Your tally gives 12 heads over 20 tosses: 12/20 = 0.6.
The whole is the whole
The whole is every toss, not part of it. "How many heads against tails?" is a different question. It gives 12 heads against 8 tails, or 12/8 = 1.5. That ratio is more than 1, so it is off the scale. Heads are part of all tosses. So heads over all tosses is at most 1.
| Question | Ratio | On the 0-to-1 scale? |
|---|---|---|
| Share of tosses that gave heads | 12/20 = 0.6 | yes |
| Heads compared with tails | 12/8 = 1.5 | no |
Rule: An observed chance is a count over a whole. It is the 's over every trial made.
Sample — a small part taken from a larger group. A sample of 40 pencils has 6 broken. A box has 500 pencils. Suppose the 40 are typical of the box. Then 6/40 = 0.15, and 0.15 × 500 = 75 broken.
Toss 20 times. Read the count.
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Try the lab to finish this lesson.