Track quiz
Eight ideas, eight checks. The table comes first, so you have somewhere to look.
| Idea | How it goes |
|---|---|
| Random | The next toss cannot be called. A whole run can be described. |
| The 0-to-1 scale | A chance is a number from 0 to 1. 0 is impossible. 1 is certain. The chances of all the outcomes of one draw add to 1. |
| Observed chance | An observed chance is a count over a whole. It is the outcome's trials over every trial made. |
| Settling | More tries steady the share. They never fully still it. Each try is blind to the ones before it. |
| Worked-out chance | Count the outcomes an event allows. Divide by all the outcomes that can happen. First check they are equally likely. |
| Two figures | Real rolls give one figure. The die's faces give another. With few rolls a gap is normal. It does not prove the die is unfair. |
| Pairs | Write the two actions as a table of pairs. Count the pairs an event holds. Divide by all the pairs. |
| Trees | One stage per choice. Multiply along a path. The paths together add to exactly 1. |
A friend calls heads on every toss of a fair coin. What happens over a long run?
A jar has 5 red, 3 blue and 2 green marbles. One is drawn. What do the three chances add to?
Twenty tosses gave 12 heads. What is the observed chance of tails?
A fair coin has landed tails four times in a row. What does that tell you about the next toss?
A jar has 5 red, 3 blue and 2 green marbles. Someone says each colour has a chance of 1/3. What is wrong?
A die is rolled 15 times and shows a 4 five times. Experimental: about 0.33. Theoretical: about 0.17. What does the gap say?
Two coins are tossed together. What is the chance that exactly one lands heads?
On the two-coin tree, what is the chance of heads then tails? What do the four paths add to?
Chapter 7, The Mathematics of Maybe, is next. Read it and see how each idea in the table grows.
Next: Predicting What Comes Next: Exploring Sequences and Progressions. From chances to rules that name every term.