Probability goes from 0 (impossible) on the left to 1 (certain) on the right, with one half in the middle. If the scale is split into equal steps, count steps from 0: 3 steps of 4 is 3/4. The same position can be written as a decimal, so 7 steps of 10 is 0.7 and 1/4 is 0.25. To place an event, count the outcomes where it happens out of all the equally likely outcomes, then find that point.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- probability
- how likely something is, from 0 to 1
- impossible
- probability 0: it cannot happen
- certain
- probability 1: it must happen
Worked examples
An arrow is 3 steps along a scale split into 4 steps. What probability?
- 1.Each step is 1/4.
- 2.3 steps is 3/4.
= 3/4
An arrow is 7 steps along a scale split into 10 steps. Write it as a decimal.
- 1.Each step is one tenth.
- 2.7 tenths is 0.7.
= 0.7
A bag has 1 red and 3 blue counters. Where is P(red)? Points: A at 1/4, B at 1/2, C at 3/4
- 1.1 of the 4 counters is red: 1/4.
- 2.The point at 1/4 is A.
= A
For parents
Method: Count the steps from 0
What to say: How many equal steps is the scale split into? How many steps from 0 is it?
Common mistakes:
- Gives the number of steps counted as a whole number, not a probability.
- Uses the number of tick marks (including the one at 0) as the denominator.
- Measures from the certain end, giving the chance of the event not happening.
- Writes tenths in the hundredths place.
- Writes a fraction's digits after the decimal point.
- Places any uncertain event at one half, because it 'either happens or it doesn't'.
- Compares favourable with unfavourable outcomes instead of with all outcomes.