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.
Adding up to 1
The probabilities of all the different outcomes add up to 1. So P(not A) = 1 − P(A), and a missing value in a probability table is 1 minus the others. For outcomes that cannot happen together, P(A or B) = P(A) + P(B).
- P(red) = 0.2, P(blue) = 0.35, P(green) = 0.15, P(yellow) = ?
- 0.2 + 0.35 + 0.15 = 0.7
- P(yellow) = 1 − 0.7 = 0.3
Expected number
To estimate how often something will happen, multiply: expected number = probability × number of trials. A spinner with P(red) = 0.3 spun 200 times should give red about 0.3 × 200 = 60 times. It is an estimate, not a promise.
Roll it many times
In the probability simulation, roll one dice 60 times. You expect about 60 × 1/6 = 10 sixes. How many did you get? Now run 6000 rolls: is the relative frequency of a six closer to 1/6?