One-page revision sheet

• Every probability lies between 0 and 1. Nothing is less likely than impossible or more likely than certain.
• 0 = impossible, 1/2 = even chance, 1 = certain.
• A probability can be written as a fraction, a decimal or a percentage — all three mean the same thing.
• 0.2 = 1/5 = 20%. Convert to one form before comparing.
• Words like “probably” mean different things to different people; a number does not.
• An outcome is one possible result; an event is the outcome or outcomes you care about.
• An event and its opposite have probabilities that add to 1.
• A probability of 1/2 does not promise that exactly half of any set of trials will succeed.

Key words: probability  ·  impossible  ·  certain  ·  even chance  ·  outcome  ·  event  ·  probability scale

• When outcomes are equally likely: P = favourable outcomes ÷ total outcomes.
• Count the total carefully — it is the denominator of every answer in the question.
• The probabilities of all possible outcomes add to 1, because something must happen.
• So P(not A) = 1 − P(A). This is often much quicker than counting.
• Two events are mutually exclusive if they cannot both happen.
• For mutually exclusive events, P(A or B) = P(A) + P(B) — no outcome gets counted twice.
• Give the answer as a fraction in its simplest form unless the question says otherwise.
• The formula only applies when the outcomes really are equally likely: a drawing pin is not a fair coin.

Key words: equally likely  ·  favourable outcome  ·  complement  ·  mutually exclusive  ·  trial  ·  random

• Theoretical probability is what should happen: favourable ÷ total.
• Experimental probability is what did happen: successes ÷ trials.
• Expected number = probability × number of trials.
• The expected number is an average, not a promise. Getting 8 sixes in 60 rolls instead of 10 is perfectly normal.
• As the number of trials grows, experimental probability usually moves closer to the theoretical value.
• A small difference is ordinary variation; a large, persistent one suggests bias.
• When outcomes are not equally likely — a drawing pin, a weighted spinner — only an experiment can give the probability.
• This is the same idea as sample size in Unit 6: more trials, more trustworthy.

Key words: experimental probability  ·  theoretical probability  ·  trial  ·  expected number  ·  bias