When every outcome is equally likely, the probability of an event is the number of outcomes you want over the total number of outcomes. A spinner with 8 equal sections, 3 of them red, gives P(red) = 3/8. Count sections or counters, not colours. For numbered cards, list the numbers that fit: 'greater than 6' does not include 6. Fractions can be simplified: 4/10 = 2/5.
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
- equally likely
- each outcome has the same chance
- favourable outcome
- an outcome that gives the event you want
- P( )
- short for 'the probability of'
Worked examples
A spinner has 8 equal sections and 3 are red. P(red)?
- 1.8 equally likely outcomes.
- 2.3 are red, so P(red) = 3/8.
= 3/8
A bag has 3 red, 5 blue and 2 green counters. P(blue)?
- 1.3 + 5 + 2 = 10 counters.
- 2.5 are blue: 5/10 = 1/2.
= 1/2
Cards 1 to 10. P(greater than 6)?
- 1.Greater than 6: 7, 8, 9, 10 (not 6).
- 2.4 out of 10 = 2/5.
= 2/5
For parents
Method: Wanted outcomes over all outcomes
What to say: How many outcomes are there altogether? How many of them are the ones we want?
Common mistakes:
- Compares the favourable outcomes with the others instead of with all of them.
- Uses the number of colours as the number of outcomes.
- Gives the chance of the event not happening.
- Uses one favourable outcome when several give the event.
- Includes the boundary number in 'greater than' or 'less than'.
- Gives one half because the event 'either happens or it doesn't'.