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Probability
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Probability measures how likely something is, from impossible (0) to certain (1).
The probability scale
Probabilities go from 0 (impossible) to 1 (certain). An even chance is 0.5.
Write them as fractions, decimals or percentages, never as '1 in 4' or '1 out of 4'.
Write them as fractions, decimals or percentages, never as '1 in 4' or '1 out of 4'.
Equally likely outcomes
P(event) = number of ways it can happentotal number of equally likely outcomes
A bag has 3 red, 5 blue and 2 green counters. P(blue) = 510 = 12.
The probabilities of all the possible outcomes add up to 1, so P(not A) = 1 − P(A).
A bag has 3 red, 5 blue and 2 green counters. P(blue) = 510 = 12.
The probabilities of all the possible outcomes add up to 1, so P(not A) = 1 − P(A).
Experiments
Relative frequency = number of times it happenednumber of trials. It estimates the probability, and gets more reliable with more trials.
If a coin lands heads much more than half the time in many trials, it may be biased (unfair).
Expected number = probability × number of trials.
If a coin lands heads much more than half the time in many trials, it may be biased (unfair).
Expected number = probability × number of trials.
A spinner has P(red) = 0.1, P(blue) = 0.35, P(green) = 0.25 and P(yellow) = x. Find x.
- All the probabilities add to 1
- 0.1 + 0.35 + 0.25 = 0.7
- x = 1 − 0.7
Answer: 0.3
P = favourable outcomes ÷ total outcomes. All probabilities add to 1, so P(not A) = 1 − P(A). Relative frequency estimates probability from experiments.
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