The big picture
A chance is a number. It comes from counting.
| Idea | Remember | Example |
|---|---|---|
| Random | The next toss cannot be called. A whole run can be described. | Coin toss before a match |
| 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. | 0.5 + 0.3 + 0.2 = 1 |
| Observed chance | An observed chance is a count over a whole. It is the outcome's trials over every trial made. | 12 heads of 20 = 0.6 |
| Settling | More tries steady the share. They never fully still it. Each try is blind to the ones before it. | 600 tosses settle near 0.5 |
| Worked-out chance | Count the outcomes an event allows. Divide by all the outcomes that can happen. First check they are equally likely. | Fair die: even number = 1/2 |
| 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. | 5/15 against 1/6 |
| Pairs | Write the two actions as a table of pairs. Count the pairs an event holds. Divide by all the pairs. | Two coins: HT, TH = 1/2 |
| Trees | One stage per choice. Multiply along a path. The paths together add to exactly 1. | 1/2 × 1/2 = 1/4 |
Open Chapter 7, The Mathematics of Maybe, in your NCERT book. You now know both ways of counting a chance. You know the table and the tree too.