Probabilities from 0 to 1, equally likely outcomes, the probability of not, probability tables and expected numbers.
What you will learn
- Work out a probability from equally likely outcomes
- Use P(not A) = 1 − P(A)
- Use the fact that probabilities add up to 1
- Work out an expected number of times
Favourable over total
When every outcome is equally likely, P(event) = number of ways it can happen ÷ total number of outcomes.
A bag with 3 red and 5 blue counters gives P(red) = 3/8. Probabilities go from 0 (impossible) to 1 (certain), and can be written as fractions, decimals or percentages.
Taking something at random means every item is equally likely to be picked. A fair dice or spinner has every outcome equally likely; a biased one does not. On a fair dice numbered 1 to 8, P(more than 5) = 3/8: the outcomes are 6, 7 and 8 ("more than 5" does not include 5).
Words on the probability scale: impossible is 0, unlikely is between 0 and 0.5, even chance is exactly 0.5, likely is between 0.5 and 1, and certain is 1.
If you add more items to a bag, the total goes up too. A bag has 4 red and 6 blue counters; after k more red counters P(red) = 1/2, so (4 + k)/(10 + k) = 1/2. Then 2(4 + k) = 10 + k, so k = 2.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Favourable over total
- Adding up to 1
- Expected number
- Try it: Roll it many times
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Fair, Impossible, Unlikely, Even chance, Likely, Certain
In this unit: Probability
Probabilities of single events, relative frequency, sample spaces, Venn diagrams and two-way tables, tree diagrams, and conditional probability.